| 1 |
C -------- |
| 2 |
CN NAME: R P P M |
| 3 |
C -------- |
| 4 | |
| 5 |
CP PURPOSE: |
| 6 |
CP SOLVE THE 1D EQUATIONS OF RELATIVISTIC HYDRODYNAMICS IN PLANAR SYMMETRY |
| 7 |
CP FOR AN IDEAL GAS EQUATION OF STATE. |
| 8 |
C |
| 9 | |
| 10 |
CC COMMENTS: |
| 11 |
CC THIS PROGRAM IS DESCRIBED IN THE PAPER BY MARTI & MUELLER, JCP, 1996. |
| 12 |
CC IT USES AN EXACT RIEMANN SOLVER (MARTI & MUELLER, JFM, 1994), PPM SPATIAL |
| 13 |
CC RECONSTRUCTION AND AVERAGING IN THE DOMAIN OF DEPENDENCE OF THE |
| 14 |
CC CELL INTERFACES FOR TIME ADVANCE. |
| 15 |
CC LIGHT SPEED IN CODE UNITS IS EQUAL TO 1. |
| 16 |
CC |
| 17 |
CC WRITTEN BY: Jose-Maria Marti |
| 18 |
CC Departamento de Astronomia y Astrofisica |
| 19 |
CC Universidad de Valencia |
| 20 |
CC 46100 Burjassot (Valencia), Spain |
| 21 |
CC jose-maria.marti@uv.es |
| 22 |
CC AND |
| 23 |
CC Ewald Mueller |
| 24 |
CC Max-Planck-Institut fuer Astrophysik |
| 25 |
CC Karl-Schwarzschild-Str. 1 |
| 26 |
CC 85741 Garching, Germany |
| 27 |
CC emueller@mpa-garching.mpg.de |
| 28 |
C |
| 29 | |
| 30 |
PROGRAM RPPM
|
| 31 | |
| 32 |
IMPLICIT NONE
|
| 33 | |
| 34 |
INCLUDE 'size'
|
| 35 | |
| 36 |
C ---------- |
| 37 |
C COMMON BLOCKS |
| 38 |
C ---------- |
| 39 | |
| 40 |
INTEGER BNDMNX,BNDMXX
|
| 41 |
COMMON /BOUN/ BNDMNX,BNDMXX
|
| 42 | |
| 43 |
INTEGER NEND,NOUT,ITSTP,NX
|
| 44 |
COMMON /INPTI/ NEND,NOUT,ITSTP,NX
|
| 45 | |
| 46 |
INTEGER NSTEP
|
| 47 |
COMMON /NSTEP/ NSTEP
|
| 48 | |
| 49 |
INTEGER NOUT1
|
| 50 |
COMMON /OUTI/ NOUT1
|
| 51 | |
| 52 |
DOUBLEPRECISION GAMMA
|
| 53 |
COMMON /ADIND/ GAMMA
|
| 54 | |
| 55 |
DOUBLEPRECISION X(-4:MN5),XL(-4:MN5),XR(-4:MN5),DX(-4:MN5)
|
| 56 |
COMMON /GRD/ X,XL,XR,DX
|
| 57 | |
| 58 |
DOUBLEPRECISION P(-4:MN5),RHO(-4:MN5),VEL(-4:MN5),W(-4:MN5),
|
| 59 |
& U(-4:MN5),CS(-4:MN5),H(-4:MN5),DPDRH(-4:MN5), |
| 60 |
& DPDU(-4:MN5),R(-4:MN5),M(-4:MN5),E(-4:MN5) |
| 61 |
COMMON /HYDRO/ P,RHO,VEL,W,U,CS,H,DPDRH,DPDU,R,M,E
|
| 62 | |
| 63 |
DOUBLEPRECISION TMAX,TOUT,CFL,DTINI,SMALL,SMLRHO,SMALLP,SMALLU,
|
| 64 |
& GRIDLX,EPSILN,ETA1,ETA2,EPSLN,AK0,OMG1,OMG2 |
| 65 |
COMMON /INPTF/ TMAX,TOUT,CFL,DTINI,SMALL,SMLRHO,SMALLP,SMALLU,
|
| 66 |
& GRIDLX,EPSILN,ETA1,ETA2,EPSLN,AK0,OMG1,OMG2 |
| 67 | |
| 68 |
DOUBLEPRECISION TOUT1
|
| 69 |
COMMON /OUTF/ TOUT1
|
| 70 | |
| 71 |
DOUBLEPRECISION TIME,DT
|
| 72 |
COMMON /ZEIT/ TIME,DT
|
| 73 | |
| 74 |
CHARACTER*7 OUTFIL
|
| 75 |
CHARACTER*8 LABEL
|
| 76 |
CHARACTER*4 BASENM
|
| 77 |
CHARACTER*2 SUFFIX
|
| 78 |
COMMON /CHRC/ LABEL,OUTFIL,BASENM,SUFFIX
|
| 79 | |
| 80 |
C -------------------- |
| 81 |
C READ INITIAL PARAMETERS |
| 82 |
C -------------------- |
| 83 | |
| 84 |
CALL INPUT
|
| 85 | |
| 86 |
C -------------------- |
| 87 |
C CONSTRUCT A NEW MODEL |
| 88 |
C -------------------- |
| 89 | |
| 90 |
IF (SUFFIX(2:2).NE.'A') THEN
|
| 91 | |
| 92 |
WRITE(6,2000)
|
| 93 |
2000 FORMAT('RPPM: CHECK INPUT FILE SUFFIX')
|
| 94 |
STOP
|
| 95 | |
| 96 |
END IF
|
| 97 | |
| 98 |
WRITE(6,2100)
|
| 99 |
2100 FORMAT('RPPM: CONSTRUCTING NEW INITIAL MODEL')
|
| 100 | |
| 101 |
CALL GRID
|
| 102 | |
| 103 |
CALL INIT
|
| 104 | |
| 105 |
CALL TSTEP
|
| 106 | |
| 107 |
DT = MIN(DT, DTINI)
|
| 108 | |
| 109 |
OUTFIL = BASENM//'O'//SUFFIX
|
| 110 | |
| 111 |
NOUT1 = 0
|
| 112 |
TOUT1 = 0.D0
|
| 113 | |
| 114 |
C ------------- |
| 115 |
C START TIME LOOP |
| 116 |
C ------------- |
| 117 | |
| 118 |
DO 100 NSTEP = 1, NEND
|
| 119 | |
| 120 |
TIME = TIME + DT
|
| 121 |
NOUT1 = NOUT1 + 1
|
| 122 |
TOUT1 = TOUT1 + DT
|
| 123 | |
| 124 |
IF (TIME.GT.TMAX) GOTO 200
|
| 125 | |
| 126 |
CALL BNDRY
|
| 127 | |
| 128 |
CALL HYDROW
|
| 129 | |
| 130 |
IF ( (NOUT1.GE.NOUT) .OR. (TOUT1.GE.TOUT)) CALL PLTOUT
|
| 131 | |
| 132 |
CALL TSTEP
|
| 133 | |
| 134 |
100 CONTINUE |
| 135 | |
| 136 |
200 CONTINUE |
| 137 | |
| 138 |
STOP 'RPPM: NORMAL TERMINATION'
|
| 139 |
END
|
| 140 | |
| 141 |
C -------- |
| 142 |
CN NAME: I N P U T |
| 143 |
C -------- |
| 144 | |
| 145 |
CP PURPOSE: |
| 146 |
CP READS THE INITIAL PARAMETERS FROM FILE inpt.dat |
| 147 |
C |
| 148 | |
| 149 |
CC COMMENTS: |
| 150 |
CC SEE INSERTED COMMENTS |
| 151 | |
| 152 |
SUBROUTINE INPUT
|
| 153 | |
| 154 |
IMPLICIT NONE
|
| 155 | |
| 156 |
INCLUDE 'size'
|
| 157 | |
| 158 |
C --------- |
| 159 |
C COMMON BLOCKS |
| 160 |
C --------- |
| 161 | |
| 162 |
INTEGER NEND,NOUT,ITSTP,NX
|
| 163 |
COMMON /INPTI/ NEND,NOUT,ITSTP,NX
|
| 164 | |
| 165 |
DOUBLEPRECISION TMAX,TOUT,CFL,DTINI,SMALL,SMLRHO,SMALLP,SMALLU,
|
| 166 |
& GRIDLX,EPSILN,ETA1,ETA2,EPSLN,AK0,OMG1,OMG2 |
| 167 |
COMMON /INPTF/ TMAX,TOUT,CFL,DTINI,SMALL,SMLRHO,SMALLP,SMALLU,
|
| 168 |
& GRIDLX,EPSILN,ETA1,ETA2,EPSLN,AK0,OMG1,OMG2 |
| 169 | |
| 170 |
CHARACTER*7 OUTFIL
|
| 171 |
CHARACTER*8 LABEL,LABEL1
|
| 172 |
CHARACTER*4 BASENM
|
| 173 |
CHARACTER*2 SUFFIX
|
| 174 |
COMMON /CHRC/ LABEL,OUTFIL,BASENM,SUFFIX
|
| 175 | |
| 176 |
C --------- |
| 177 |
C INTERNAL VARIABLES |
| 178 |
C --------- |
| 179 | |
| 180 |
CHARACTER*72 TEXT
|
| 181 |
CHARACTER*2 TXT
|
| 182 |
CHARACTER*15 TXTXT
|
| 183 |
DATA TXTXT /'............. '/
|
| 184 | |
| 185 |
OPEN(1,FILE='inpt.dat',FORM='FORMATTED',STATUS='OLD')
|
| 186 | |
| 187 |
READ (1,*) TEXT
|
| 188 |
WRITE(6,*) TEXT
|
| 189 |
READ (1,*) TEXT
|
| 190 |
WRITE(6,*) TEXT
|
| 191 |
READ (1,*) TEXT
|
| 192 |
WRITE(6,*) TEXT
|
| 193 |
PRINT*, '-------------------------------------------------------'
|
| 194 | |
| 195 |
C ---------------------------- |
| 196 |
C BASENM IS THE ROOT FOR THE OUTPUT, PLOT AND RESTART FILE NAMES (ROOTS |
| 197 |
C RST_, RBW_, RSR_, RBWI STAND FOR SPECIAL TESTS) |
| 198 |
C ---------------------------- |
| 199 | |
| 200 |
READ (1,*) TXT,LABEL,BASENM
|
| 201 |
WRITE(6,*) TXT,LABEL,TXTXT,BASENM
|
| 202 |
LABEL1 = 'basenm'
|
| 203 |
IF (LABEL.NE.LABEL1) GOTO 10
|
| 204 | |
| 205 |
C ---------------------------- |
| 206 |
C NEND IS THE TOTAL NUMBER OF TIMESTEPS |
| 207 |
C ---------------------------- |
| 208 | |
| 209 |
READ (1,*) TXT,LABEL,NEND
|
| 210 |
WRITE(6,*) TXT,LABEL,TXTXT,NEND
|
| 211 |
LABEL1 = 'nend'
|
| 212 |
IF (LABEL.NE.LABEL1) GOTO 10
|
| 213 | |
| 214 |
C ---------------------------- |
| 215 |
C THE PROGRAM STOPS WHEN TIME IS .GE. THAN TMAX |
| 216 |
C ---------------------------- |
| 217 | |
| 218 |
READ (1,*) TXT,LABEL,TMAX
|
| 219 |
WRITE(6,*) TXT,LABEL,TXTXT,TMAX
|
| 220 |
LABEL1 = 'tmax'
|
| 221 |
IF (LABEL.NE.LABEL1) GOTO 10
|
| 222 | |
| 223 |
C ---------------------------- |
| 224 |
C SUFFIX IS THE SUFFIX FOR THE OUTPUT AND RESTART FILE NAMES |
| 225 |
C ---------------------------- |
| 226 | |
| 227 |
READ (1,*) TXT,LABEL,SUFFIX
|
| 228 |
WRITE(6,*) TXT,LABEL,TXTXT,SUFFIX
|
| 229 |
LABEL1 = 'suffix'
|
| 230 |
IF (LABEL.NE.LABEL1) GOTO 10
|
| 231 | |
| 232 |
C ---------------------------- |
| 233 |
C AN OUTPUT FILE IS WRITEN EVERY NOUT TIMESTEPS |
| 234 |
C ---------------------------- |
| 235 | |
| 236 |
READ (1,*) TXT,LABEL,NOUT
|
| 237 |
WRITE(6,*) TXT,LABEL,TXTXT,NOUT
|
| 238 |
LABEL1 = 'nout'
|
| 239 |
IF (LABEL.NE.LABEL1) GOTO 10
|
| 240 | |
| 241 |
C ---------------------------- |
| 242 |
C AN OUTPUT FILE IS WRITEN EVERY TOUT TIME UNITS |
| 243 |
C ---------------------------- |
| 244 | |
| 245 |
READ (1,*) TXT,LABEL,TOUT
|
| 246 |
WRITE(6,*) TXT,LABEL,TXTXT,TOUT
|
| 247 |
LABEL1 = 'tout'
|
| 248 |
IF (LABEL.NE.LABEL1) GOTO 10
|
| 249 | |
| 250 |
C ----------------------------- |
| 251 |
C DT IS WRITEN ON THE SCREEN EVERY ITSTP TIMESTEPS |
| 252 |
C ----------------------------- |
| 253 | |
| 254 |
READ (1,*) TXT,LABEL,ITSTP
|
| 255 |
WRITE(6,*) TXT,LABEL,TXTXT,ITSTP
|
| 256 |
LABEL1 = 'itstp'
|
| 257 |
IF (LABEL.NE.LABEL1) GOTO 10
|
| 258 | |
| 259 |
C ----------------------------- |
| 260 |
C CFL IS THE TIME-LIMITING FACTOR (.LT. 1) |
| 261 |
C ----------------------------- |
| 262 | |
| 263 |
READ (1,*) TXT,LABEL,CFL
|
| 264 |
WRITE(6,*) TXT,LABEL,TXTXT,CFL
|
| 265 |
LABEL1 = 'cfl'
|
| 266 |
IF (LABEL.NE.LABEL1) GOTO 10
|
| 267 | |
| 268 |
C ------------------- |
| 269 |
C DTINI IS THE INITIAL DT |
| 270 |
C ------------------- |
| 271 | |
| 272 |
READ (1,*) TXT,LABEL,DTINI
|
| 273 |
WRITE(6,*) TXT,LABEL,TXTXT,DTINI
|
| 274 |
LABEL1 = 'dtini'
|
| 275 |
IF (LABEL.NE.LABEL1) GOTO 10
|
| 276 | |
| 277 |
C ------------------------------------------- |
| 278 |
C SMALL IS THE THRESHOLD FOR NONDIMENSIONAL NUMBERS (I.E. VELOCITY) |
| 279 |
C ------------------------------------------- |
| 280 | |
| 281 |
READ (1,*) TXT,LABEL,SMALL
|
| 282 |
WRITE(6,*) TXT,LABEL,TXTXT,SMALL
|
| 283 |
LABEL1 = 'small'
|
| 284 |
IF (LABEL.NE.LABEL1) GOTO 10
|
| 285 | |
| 286 |
C ----------------------------------------- |
| 287 |
C SMLRHO IS THE THRESHOLD FOR DENSITIES (RHO, R) |
| 288 |
C ----------------------------------------- |
| 289 | |
| 290 |
READ (1,*) TXT,LABEL,SMLRHO
|
| 291 |
WRITE(6,*) TXT,LABEL,TXTXT,SMLRHO
|
| 292 |
LABEL1 = 'smlrho'
|
| 293 |
IF (LABEL.NE.LABEL1) GOTO 10
|
| 294 | |
| 295 |
C -------------------------------- |
| 296 |
C SMALLP IS THE THRESHOLD FOR PRESSURE |
| 297 |
C -------------------------------- |
| 298 | |
| 299 |
READ (1,*) TXT,LABEL,SMALLP
|
| 300 |
WRITE(6,*) TXT,LABEL,TXTXT,SMALLP
|
| 301 |
LABEL1 = 'smallp'
|
| 302 |
IF (LABEL.NE.LABEL1) GOTO 10
|
| 303 | |
| 304 |
C --------------------------------- |
| 305 |
C SMALLU IS THE THRESHOLD FOR INTERNAL ENERGY |
| 306 |
C --------------------------------- |
| 307 | |
| 308 |
READ (1,*) TXT,LABEL,SMALLU
|
| 309 |
WRITE(6,*) TXT,LABEL,TXTXT,SMALLU
|
| 310 |
LABEL1 = 'smallu'
|
| 311 |
IF (LABEL.NE.LABEL1) GOTO 10
|
| 312 | |
| 313 |
C ------------------------ |
| 314 |
C GRIDLX IS THE LENGTH OF THE GRID |
| 315 |
C ------------------------ |
| 316 | |
| 317 |
READ (1,*) TXT,LABEL,GRIDLX
|
| 318 |
WRITE(6,*) TXT,LABEL,TXTXT,GRIDLX
|
| 319 |
LABEL1 = 'gridlx'
|
| 320 |
IF (LABEL.NE.LABEL1) GOTO 10
|
| 321 | |
| 322 |
IF ((BASENM.EQ.'RST_'.OR.BASENM.EQ.'RBW_'.OR.BASENM.EQ.'RSR_'.OR.
|
| 323 |
& BASENM.EQ.'RBWI').AND. |
| 324 |
& GRIDLX.NE.1.D0) THEN |
| 325 | |
| 326 |
GRIDLX = 1.D0
|
| 327 |
WRITE(6,1200)
|
| 328 |
1200 FORMAT('INPUT: GRIDLX RESET TO 1.D0')
|
| 329 | |
| 330 |
END IF
|
| 331 | |
| 332 |
C --------------------------- |
| 333 |
C NX IS THE NUMBER OF GRID POINTS |
| 334 |
C --------------------------- |
| 335 | |
| 336 |
READ (1,*) TXT,LABEL,NX
|
| 337 |
WRITE(6,*) TXT,LABEL,TXTXT,NX
|
| 338 |
LABEL1 = 'nx'
|
| 339 |
IF (LABEL.NE.LABEL1) GOTO 10
|
| 340 | |
| 341 |
IF (NX.LT.4.OR.NX.GT.MNX) STOP 'INPUT: UNSUITABLE NX'
|
| 342 | |
| 343 |
C ---------------------------------------- |
| 344 |
C ETA1 IS USED IN SUBROUTINE DETECT (PPM RECONSTRUCTION) |
| 345 |
C TYPICAL VALUE: 5.D0 |
| 346 |
C ---------------------------------------- |
| 347 | |
| 348 |
READ (1,*) TXT,LABEL,ETA1
|
| 349 |
WRITE(6,*) TXT,LABEL,TXTXT,ETA1
|
| 350 |
LABEL1 = 'eta1'
|
| 351 |
IF (LABEL.NE.LABEL1) GOTO 10
|
| 352 | |
| 353 |
C ------------------------------------------- |
| 354 |
C ETA2 IS USED IN SUBROUTINE DETECT (PPM RECONSTRUCTION) |
| 355 |
C TYPICAL VALUE: 5.D-2 |
| 356 |
C ------------------------------------------- |
| 357 | |
| 358 |
READ (1,*) TXT,LABEL,ETA2
|
| 359 |
WRITE(6,*) TXT,LABEL,TXTXT,ETA2
|
| 360 |
LABEL1 = 'eta2'
|
| 361 |
IF (LABEL.NE.LABEL1) GOTO 10
|
| 362 | |
| 363 |
C --------------------------------------- |
| 364 |
C EPSLN IS USED IN SUBROUTINE DETECT (PPM RECONSTRUCTION) |
| 365 |
C TYPICAL VALUE: 1.D-1 |
| 366 |
C --------------------------------------- |
| 367 | |
| 368 |
READ (1,*) TXT,LABEL,EPSLN
|
| 369 |
WRITE(6,*) TXT,LABEL,TXTXT,EPSLN
|
| 370 |
LABEL1 = 'epsln'
|
| 371 |
IF (LABEL.NE.LABEL1) GOTO 10
|
| 372 | |
| 373 |
C ----------------------------------------- |
| 374 |
C AK0 IS USED IN SUBROUTINE DETECT (PPM RECONSTRUCTION) |
| 375 |
C TYPICAL VALUE: 1.D0 |
| 376 |
C ----------------------------------------- |
| 377 |
READ (1,*) TXT,LABEL,AK0
|
| 378 |
WRITE(6,*) TXT,LABEL,TXTXT,AK0
|
| 379 |
LABEL1 = 'ak0'
|
| 380 |
IF (LABEL.NE.LABEL1) GOTO 10
|
| 381 | |
| 382 |
C ---------------------------------------- |
| 383 |
C EPSILN IS USED IN SUBROUTINE FLATEN (PPM RECONSTRUCTION) |
| 384 |
C TYPICAL VALUE: 1.D0 |
| 385 |
C ---------------------------------------- |
| 386 | |
| 387 |
READ (1,*) TXT,LABEL,EPSILN
|
| 388 |
WRITE(6,*) TXT,LABEL,TXTXT,EPSILN
|
| 389 |
LABEL1 = 'epsiln'
|
| 390 |
IF (LABEL.NE.LABEL1) GOTO 10
|
| 391 | |
| 392 |
C --------------------------------------- |
| 393 |
C OMG1 IS USED IN SUBROUTINE FLATEN (PPM RECONSTRUCTION) |
| 394 |
C TYPICAL VALUE: 5.2D-1 |
| 395 |
C --------------------------------------- |
| 396 | |
| 397 |
READ (1,*) TXT,LABEL,OMG1
|
| 398 |
WRITE(6,*) TXT,LABEL,TXTXT,OMG1
|
| 399 |
LABEL1 = 'omg1'
|
| 400 |
IF (LABEL.NE.LABEL1) GOTO 10
|
| 401 | |
| 402 |
C ---------------------------------------- |
| 403 |
C OMG2 IS USED IN SUBROUTINE FLATEN (PPM RECONSTRUCTION) |
| 404 |
C TYPICAL VALUE: 1.D1 |
| 405 |
C ---------------------------------------- |
| 406 | |
| 407 |
READ (1,*) TXT,LABEL,OMG2
|
| 408 |
WRITE(6,*) TXT,LABEL,TXTXT,OMG2
|
| 409 |
LABEL1 = 'omg2'
|
| 410 |
IF (LABEL.NE.LABEL1) GOTO 10
|
| 411 | |
| 412 |
PRINT*, '-------------------------------------------------------'
|
| 413 | |
| 414 |
RETURN
|
| 415 | |
| 416 |
10 CONTINUE |
| 417 |
PRINT*, ' '
|
| 418 |
WRITE(6,1020)
|
| 419 |
1020 FORMAT('INPUT: INCORRECT INPUT DECK')
|
| 420 |
WRITE(6,1001) LABEL, LABEL1
|
| 421 |
1001 FORMAT(' LABEL = ',A6,' EXPECTED LABEL = ',A6)
|
| 422 |
STOP
|
| 423 | |
| 424 |
END
|
| 425 | |
| 426 |
C -------- |
| 427 |
CN NAME: G R I D |
| 428 |
C -------- |
| 429 | |
| 430 |
CP PURPOSE: |
| 431 |
CP ESTABLISHES THE BOUNDARY CONDITIONS AND SETS UP THE NUMERICAL GRID |
| 432 |
C |
| 433 | |
| 434 |
CC COMMENTS: |
| 435 |
CC BOUNDARY CONDITIONS ARE SPECIFIED FOR A SERIES OF 1D TESTS. BOUNDARIES. |
| 436 |
CC APPROPRIATE BOUNDARIES MUST BE CHOSEN BY THE USER FOR SPECIFIC PROBLEMS. |
| 437 |
CC AN EQUIDISTANT X-GRID IS GENERATED BY DEFAULT, HOWEVER THE CODE IS |
| 438 |
CC SUITED FOR NON-EQUIDISTANT GRIDS |
| 439 | |
| 440 |
SUBROUTINE GRID
|
| 441 | |
| 442 |
IMPLICIT NONE
|
| 443 | |
| 444 |
INCLUDE 'size'
|
| 445 | |
| 446 |
C ---------- |
| 447 |
C COMMON BLOCKS |
| 448 |
C ---------- |
| 449 | |
| 450 |
INTEGER BNDMNX,BNDMXX
|
| 451 |
COMMON /BOUN/ BNDMNX,BNDMXX
|
| 452 | |
| 453 |
INTEGER NEND,NOUT,ITSTP,NX
|
| 454 |
COMMON /INPTI/ NEND,NOUT,ITSTP,NX
|
| 455 | |
| 456 |
DOUBLEPRECISION X(-4:MN5),XL(-4:MN5),XR(-4:MN5),DX(-4:MN5)
|
| 457 |
COMMON /GRD/ X,XL,XR,DX
|
| 458 | |
| 459 |
DOUBLEPRECISION TMAX,TOUT,CFL,DTINI,SMALL,SMLRHO,SMALLP,SMALLU,
|
| 460 |
& GRIDLX,EPSILN,ETA1,ETA2,EPSLN,AK0,OMG1,OMG2 |
| 461 |
COMMON /INPTF/ TMAX,TOUT,CFL,DTINI,SMALL,SMLRHO,SMALLP,SMALLU,
|
| 462 |
& GRIDLX,EPSILN,ETA1,ETA2,EPSLN,AK0,OMG1,OMG2 |
| 463 | |
| 464 |
CHARACTER*7 OUTFIL
|
| 465 |
CHARACTER*8 LABEL
|
| 466 |
CHARACTER*4 BASENM
|
| 467 |
CHARACTER*2 SUFFIX
|
| 468 |
COMMON /CHRC/ LABEL,OUTFIL,BASENM,SUFFIX
|
| 469 | |
| 470 |
C ------------- |
| 471 |
C INTERNAL VARIABLES |
| 472 |
C ------------- |
| 473 | |
| 474 |
INTEGER I
|
| 475 | |
| 476 |
DOUBLEPRECISION DELX
|
| 477 | |
| 478 |
C --------------------------------- |
| 479 |
C BOUNDARY CONDITIONS |
| 480 |
C BNDM.. = 1 ===> REFLECTING BOUNDARY |
| 481 |
C BNDM.. = 2 ===> FLOW OUT BOUNDARY |
| 482 |
C BNDM.. = 3 ===> FLOW IN BOUNDARY |
| 483 |
C BNDM.. = 4 ===> PERIODIC BOUNDARY |
| 484 |
C BNDM.. = 5 ===> ANY OTHER BOUNDARY |
| 485 |
C --------------------------------- |
| 486 | |
| 487 |
IF (BASENM.EQ.'RST_'.OR.BASENM.EQ.'RBW_'.OR.BASENM.EQ.'RBWI') THEN
|
| 488 |
BNDMNX = 2
|
| 489 |
BNDMXX = 2
|
| 490 |
ELSE IF (BASENM.EQ.'RSR_') THEN
|
| 491 |
BNDMNX = 2
|
| 492 |
BNDMXX = 1
|
| 493 |
ELSE
|
| 494 |
BNDMNX = 2
|
| 495 |
BNDMXX = 2
|
| 496 |
END IF
|
| 497 | |
| 498 |
IF (BNDMNX.EQ.4.AND.BNDMXX.NE.4) STOP 'GRID: INCORRECT BOUNDARIES'
|
| 499 | |
| 500 |
C ---------- |
| 501 |
C SET UP X-GRID |
| 502 |
C ---------- |
| 503 | |
| 504 |
X(1) = 0.D0
|
| 505 | |
| 506 |
DELX = GRIDLX/DFLOAT(NX)
|
| 507 | |
| 508 |
DO 10 I=2,NX+1
|
| 509 |
XL(I) = XL(I-1) + DELX
|
| 510 |
10 CONTINUE |
| 511 | |
| 512 | |
| 513 |
DO 20 I=1,NX
|
| 514 |
XR(I) = XL(I+1)
|
| 515 |
20 CONTINUE |
| 516 | |
| 517 |
DO 30 I=1,NX
|
| 518 |
X(I) = 0.5D0*(XL(I) + XR(I))
|
| 519 |
30 CONTINUE |
| 520 | |
| 521 |
DO 40 I=1,NX
|
| 522 |
DX(I) = XR(I) - XL(I)
|
| 523 |
40 CONTINUE |
| 524 | |
| 525 |
RETURN
|
| 526 |
END
|
| 527 | |
| 528 |
C -------- |
| 529 |
CN NAME: I N I T |
| 530 |
C -------- |
| 531 | |
| 532 |
CP PURPOSE: |
| 533 |
CP DEFINES THE INITIAL MODEL |
| 534 |
C |
| 535 | |
| 536 |
CC COMMENTS: |
| 537 |
CC DEFINES INITIAL DATA FOR A SERIES OF STANDARD 1D TEST PROBLEMS. |
| 538 |
CC APPROPRIATE INITIAL DATA MUST BE DEFINED BY THE USER FOR SPECIFIC |
| 539 |
CC PROBLEMS. |
| 540 |
|
| 541 |
SUBROUTINE INIT
|
| 542 | |
| 543 |
IMPLICIT NONE
|
| 544 | |
| 545 |
INCLUDE 'size'
|
| 546 | |
| 547 |
C ----------- |
| 548 |
C COMMON BLOCKS |
| 549 |
C ----------- |
| 550 | |
| 551 |
INTEGER NEND,NOUT,ITSTP,NX
|
| 552 |
COMMON /INPTI/ NEND,NOUT,ITSTP,NX
|
| 553 | |
| 554 |
DOUBLEPRECISION GAMMA
|
| 555 |
COMMON /ADIND/ GAMMA
|
| 556 | |
| 557 |
DOUBLEPRECISION X(-4:MN5),XL(-4:MN5),XR(-4:MN5),DX(-4:MN5)
|
| 558 |
COMMON /GRD/ X,XL,XR,DX
|
| 559 | |
| 560 |
DOUBLEPRECISION P(-4:MN5),RHO(-4:MN5),VEL(-4:MN5),W(-4:MN5),
|
| 561 |
& U(-4:MN5),CS(-4:MN5),H(-4:MN5),DPDRH(-4:MN5), |
| 562 |
& DPDU(-4:MN5),R(-4:MN5),M(-4:MN5),E(-4:MN5) |
| 563 |
COMMON /HYDRO/ P,RHO,VEL,W,U,CS,H,DPDRH,DPDU,R,M,E
|
| 564 | |
| 565 |
DOUBLEPRECISION TMAX,TOUT,CFL,DTINI,SMALL,SMLRHO,SMALLP,SMALLU,
|
| 566 |
& GRIDLX,EPSILN,ETA1,ETA2,EPSLN,AK0,OMG1,OMG2 |
| 567 |
COMMON /INPTF/ TMAX,TOUT,CFL,DTINI,SMALL,SMLRHO,SMALLP,SMALLU,
|
| 568 |
& GRIDLX,EPSILN,ETA1,ETA2,EPSLN,AK0,OMG1,OMG2 |
| 569 | |
| 570 |
DOUBLEPRECISION TIME,DT
|
| 571 |
COMMON /ZEIT/ TIME,DT
|
| 572 | |
| 573 |
CHARACTER*7 OUTFIL
|
| 574 |
CHARACTER*8 LABEL
|
| 575 |
CHARACTER*4 BASENM
|
| 576 |
CHARACTER*2 SUFFIX
|
| 577 |
COMMON /CHRC/ LABEL,OUTFIL,BASENM,SUFFIX
|
| 578 | |
| 579 |
C ----------- |
| 580 |
C INTERNAL VARIABLES |
| 581 |
C ----------- |
| 582 | |
| 583 |
INTEGER I
|
| 584 | |
| 585 |
C --------- |
| 586 |
C INITIAL TIME |
| 587 |
C --------- |
| 588 | |
| 589 |
TIME = 0.D0
|
| 590 | |
| 591 |
C --------------------- |
| 592 |
C RELATIVISTIC SOD'S TUBE |
| 593 |
C --------------------- |
| 594 | |
| 595 |
IF (BASENM.EQ.'RST_') THEN
|
| 596 | |
| 597 |
GAMMA = 1.4D0
|
| 598 |
|
| 599 |
DO 100 I=1,NX
|
| 600 | |
| 601 |
IF (X(I).LE.GRIDLX/2.D0) THEN
|
| 602 |
VEL(I) = 0.D0
|
| 603 |
RHO(I) = 1.D0
|
| 604 |
U(I) = 2.5D0
|
| 605 |
ELSE
|
| 606 |
VEL(I) = 0.D0
|
| 607 |
RHO(I) = 0.125D0
|
| 608 |
U(I) = 2.D0
|
| 609 |
END IF
|
| 610 | |
| 611 |
100 CONTINUE |
| 612 | |
| 613 |
GOTO 450
|
| 614 | |
| 615 |
END IF
|
| 616 | |
| 617 |
C ---------------------- |
| 618 |
C SCHNEIDER ET AL.'S TEST |
| 619 |
C ---------------------- |
| 620 | |
| 621 |
IF (BASENM.EQ.'SCHN') THEN
|
| 622 | |
| 623 |
GAMMA = 5.D0/3.D0
|
| 624 |
|
| 625 |
DO 125 I=1,NX
|
| 626 | |
| 627 |
IF (X(I).LE.GRIDLX/2.D0) THEN
|
| 628 |
VEL(I) = 0.D0
|
| 629 |
RHO(I) = 10.D0
|
| 630 |
U(I) = 2.D0
|
| 631 |
ELSE
|
| 632 |
VEL(I) = 0.D0
|
| 633 |
RHO(I) = 1.D0
|
| 634 |
U(I) = 1.D-6
|
| 635 |
END IF
|
| 636 | |
| 637 |
125 CONTINUE |
| 638 | |
| 639 |
GOTO 450
|
| 640 | |
| 641 |
END IF
|
| 642 | |
| 643 |
C -------------------- |
| 644 |
C RELATIVISTIC BLAST WAVE |
| 645 |
C -------------------- |
| 646 | |
| 647 |
IF (BASENM.EQ.'RBW_') THEN
|
| 648 | |
| 649 |
GAMMA = 5.D0/3.D0
|
| 650 | |
| 651 |
DO 200 I=1,NX
|
| 652 | |
| 653 |
IF (X(I).LE.GRIDLX/2.D0) THEN
|
| 654 |
VEL(I) = 0.D0
|
| 655 |
RHO(I) = 1.D0
|
| 656 |
U(I) = 1.5D3
|
| 657 |
ELSE
|
| 658 |
VEL(I) = 0.D0
|
| 659 |
RHO(I) = 1.D0
|
| 660 |
U(I) = 1.5D-2
|
| 661 |
END IF
|
| 662 | |
| 663 |
200 CONTINUE |
| 664 | |
| 665 |
GOTO 450
|
| 666 | |
| 667 |
END IF
|
| 668 | |
| 669 |
C ----------------------- |
| 670 |
C RELATIVISTIC SHOCK REFLECTION |
| 671 |
C ----------------------- |
| 672 | |
| 673 |
IF (BASENM.EQ.'RSR_') THEN
|
| 674 | |
| 675 |
GAMMA = 4.D0/3.D0
|
| 676 |
|
| 677 |
DO 300 I=1,NX
|
| 678 | |
| 679 |
VEL(I) = 0.99999D0
|
| 680 |
RHO(I) = 1.D0
|
| 681 |
U(I) = 1.D-7/DSQRT(1.D0 - VEL(I)*VEL(I))
|
| 682 | |
| 683 |
300 CONTINUE |
| 684 | |
| 685 |
GOTO 450
|
| 686 | |
| 687 |
END IF
|
| 688 | |
| 689 |
C ------------------------ |
| 690 |
C RELATIVISTIC BLAST WAVE INTERACTION |
| 691 |
C ------------------------ |
| 692 | |
| 693 |
IF (BASENM.EQ.'RBWI') THEN
|
| 694 | |
| 695 |
GAMMA = 1.4D0
|
| 696 |
|
| 697 |
DO 400 I=1,NX
|
| 698 | |
| 699 |
IF (X(I).LE.0.1D0*GRIDLX) THEN
|
| 700 |
VEL(I) = 0.D0
|
| 701 |
RHO(I) = 1.D0
|
| 702 |
U(I) = 2.5D3
|
| 703 |
ELSE IF (X(I).LE.0.9D0*GRIDLX) THEN
|
| 704 |
VEL(I) = 0.D0
|
| 705 |
RHO(I) = 1.D0
|
| 706 |
U(I) = 2.5D-2
|
| 707 |
ELSE
|
| 708 |
VEL(I) = 0.D0
|
| 709 |
RHO(I) = 1.D0
|
| 710 |
U(I) = 2.5D2
|
| 711 |
END IF
|
| 712 | |
| 713 |
400 CONTINUE |
| 714 | |
| 715 |
GOTO 450
|
| 716 |
END IF
|
| 717 |
|
| 718 |
STOP 'INIT: NO INITIAL DATA SPECIFIED'
|
| 719 | |
| 720 |
450 CONTINUE |
| 721 | |
| 722 |
CALL EOS (NX, RHO, U, GAMMA, P, H, CS, DPDRH, DPDU)
|
| 723 | |
| 724 |
DO 500 I=1,NX
|
| 725 | |
| 726 |
W(I) = 1.D0/DSQRT(1.D0 - VEL(I)*VEL(I))
|
| 727 |
|
| 728 |
R(I) = RHO(I)*W(I)
|
| 729 |
M(I) = R(I)*H(I)*W(I)*VEL(I)
|
| 730 |
E(I) = R(I)*H(I)*W(I) - P(I) - R(I)
|
| 731 | |
| 732 |
500 CONTINUE |
| 733 | |
| 734 |
RETURN
|
| 735 |
END
|
| 736 | |
| 737 |
C -------- |
| 738 |
CN NAME: T S T E P |
| 739 |
C -------- |
| 740 | |
| 741 |
CP PURPOSE: |
| 742 |
CP COMPUTES THE NEW TIMESTEP VALUE FROM COURANT CONDITION |
| 743 |
C |
| 744 | |
| 745 |
CC COMMENTS: |
| 746 |
CC NONE |
| 747 | |
| 748 |
SUBROUTINE TSTEP
|
| 749 | |
| 750 |
IMPLICIT NONE
|
| 751 | |
| 752 |
INCLUDE 'size'
|
| 753 | |
| 754 |
C ----------- |
| 755 |
C COMMON BLOCKS |
| 756 |
C ----------- |
| 757 | |
| 758 |
INTEGER NEND,NOUT,ITSTP,NX
|
| 759 |
COMMON /INPTI/ NEND,NOUT,ITSTP,NX
|
| 760 | |
| 761 |
INTEGER NSTEP
|
| 762 |
COMMON /NSTEP/ NSTEP
|
| 763 | |
| 764 |
DOUBLEPRECISION X(-4:MN5),XL(-4:MN5),XR(-4:MN5),DX(-4:MN5)
|
| 765 |
COMMON /GRD/ X,XL,XR,DX
|
| 766 | |
| 767 |
DOUBLEPRECISION P(-4:MN5),RHO(-4:MN5),VEL(-4:MN5),W(-4:MN5),
|
| 768 |
& U(-4:MN5),CS(-4:MN5),H(-4:MN5),DPDRH(-4:MN5), |
| 769 |
& DPDU(-4:MN5),R(-4:MN5),M(-4:MN5),E(-4:MN5) |
| 770 |
COMMON /HYDRO/ P,RHO,VEL,W,U,CS,H,DPDRH,DPDU,R,M,E
|
| 771 | |
| 772 |
DOUBLEPRECISION TMAX,TOUT,CFL,DTINI,SMALL,SMLRHO,SMALLP,SMALLU,
|
| 773 |
& GRIDLX,EPSILN,ETA1,ETA2,EPSLN,AK0,OMG1,OMG2 |
| 774 |
COMMON /INPTF/ TMAX,TOUT,CFL,DTINI,SMALL,SMLRHO,SMALLP,SMALLU,
|
| 775 |
& GRIDLX,EPSILN,ETA1,ETA2,EPSLN,AK0,OMG1,OMG2 |
| 776 | |
| 777 |
DOUBLEPRECISION TIME,DT
|
| 778 |
COMMON /ZEIT/ TIME,DT
|
| 779 | |
| 780 |
C ------------ |
| 781 |
C INTERNAL VARIABLES |
| 782 |
C ------------ |
| 783 | |
| 784 |
INTEGER I,IC
|
| 785 | |
| 786 |
DOUBLEPRECISION DTCC,DTEST(MN)
|
| 787 | |
| 788 |
DOUBLEPRECISION LAMBD1,LAMBD4,LAMBDA
|
| 789 | |
| 790 |
DOUBLEPRECISION V
|
| 791 | |
| 792 |
IC = 0
|
| 793 |
DTCC = 0.D0
|
| 794 | |
| 795 |
DO 10 I=1,NX
|
| 796 | |
| 797 |
LAMBD1 = (VEL(I) - CS(I))/(1.D0 - VEL(I)*CS(I))
|
| 798 |
LAMBD4 = (VEL(I) + CS(I))/(1.D0 + VEL(I)*CS(I))
|
| 799 |
LAMBDA = DMAX1(DABS(LAMBD1),DABS(LAMBD4))
|
| 800 |
DTEST(I) = LAMBDA/(XR(I) - XL(I))
|
| 801 | |
| 802 |
10 CONTINUE |
| 803 | |
| 804 |
DO 13 I=1,NX
|
| 805 | |
| 806 |
IF (DTEST(I).GT.DTCC) THEN
|
| 807 |
IC = I
|
| 808 |
DTCC = DTEST(I)
|
| 809 |
END IF
|
| 810 | |
| 811 |
13 CONTINUE |
| 812 | |
| 813 |
DT = CFL/DTCC
|
| 814 | |
| 815 |
V = DABS(VEL(IC))
|
| 816 | |
| 817 |
IF (MOD(NSTEP,ITSTP).NE.0) RETURN
|
| 818 | |
| 819 |
WRITE(6,1001) NSTEP,DT,IC,CS(IC),V
|
| 820 | |
| 821 |
1001 FORMAT(I5,2X,1PE8.1,2X,I5,2X,1P2E11.2,2X,1P2E11.2) |
| 822 | |
| 823 |
RETURN
|
| 824 |
END
|
| 825 | |
| 826 |
C -------- |
| 827 |
CN NAME: B N D R Y |
| 828 |
C -------- |
| 829 | |
| 830 |
CP PURPOSE: |
| 831 |
CP PROVIDES DIFFERENT TYPES OF BOUNDARY CONDITIONS |
| 832 |
C |
| 833 | |
| 834 |
CC COMMENTS: |
| 835 |
CC NEW BOUNDARY CONDITIONS CAN BE SPECIFIED AT THE USER'S WILL |
| 836 | |
| 837 |
SUBROUTINE BNDRY
|
| 838 | |
| 839 |
IMPLICIT NONE
|
| 840 | |
| 841 |
INCLUDE 'size'
|
| 842 | |
| 843 |
C -------- |
| 844 |
C COMMON BLOCKS |
| 845 |
C -------- |
| 846 | |
| 847 |
INTEGER BNDMNX,BNDMXX
|
| 848 |
COMMON /BOUN/ BNDMNX,BNDMXX
|
| 849 | |
| 850 |
INTEGER NEND,NOUT,ITSTP,NX
|
| 851 |
COMMON /INPTI/ NEND,NOUT,ITSTP,NX
|
| 852 | |
| 853 |
DOUBLEPRECISION X(-4:MN5),XL(-4:MN5),XR(-4:MN5),DX(-4:MN5)
|
| 854 |
COMMON /GRD/ X,XL,XR,DX
|
| 855 | |
| 856 |
DOUBLEPRECISION P(-4:MN5),RHO(-4:MN5),VEL(-4:MN5),W(-4:MN5),
|
| 857 |
& U(-4:MN5),CS(-4:MN5),H(-4:MN5),DPDRH(-4:MN5), |
| 858 |
& DPDU(-4:MN5),R(-4:MN5),M(-4:MN5),E(-4:MN5) |
| 859 |
COMMON /HYDRO/ P,RHO,VEL,W,U,CS,H,DPDRH,DPDU,R,M,E
|
| 860 | |
| 861 |
DOUBLEPRECISION TIME,DT
|
| 862 |
COMMON /ZEIT/ TIME,DT
|
| 863 |
|
| 864 |
C --------- |
| 865 |
C INTERNAL VARIABLES |
| 866 |
C --------- |
| 867 | |
| 868 |
INTEGER I
|
| 869 | |
| 870 |
C ------------ |
| 871 |
C LEFT BOUNDARY |
| 872 |
C ------------ |
| 873 | |
| 874 |
GOTO (410, 420, 430, 440, 450), BNDMNX
|
| 875 | |
| 876 |
C ----------------- |
| 877 |
C REFLECTING BOUNDARY |
| 878 |
C ----------------- |
| 879 | |
| 880 |
410 CONTINUE |
| 881 | |
| 882 |
DO 415 I=-4,0
|
| 883 | |
| 884 |
RHO(I) = RHO(1-I)
|
| 885 |
VEL(I) = -VEL(1-I)
|
| 886 |
U(I) = U(1-I)
|
| 887 |
P(I) = P(1-I)
|
| 888 |
CS(I) = CS(1-I)
|
| 889 |
H(I) = H(1-I)
|
| 890 |
W(I) = W(1-I)
|
| 891 |
DX(I) = DX(1-I)
|
| 892 | |
| 893 |
415 CONTINUE |
| 894 | |
| 895 |
GOTO 500
|
| 896 | |
| 897 |
C --------------- |
| 898 |
C FLOW OUT BOUNDARY |
| 899 |
C --------------- |
| 900 | |
| 901 |
420 CONTINUE |
| 902 | |
| 903 |
DO 425 I=-4,0
|
| 904 | |
| 905 |
RHO(I) = RHO(1)
|
| 906 |
VEL(I) = VEL(1)
|
| 907 |
U(I) = U(1)
|
| 908 |
P(I) = P(1)
|
| 909 |
CS(I) = CS(1)
|
| 910 |
H(I) = H(1)
|
| 911 |
W(I) = W(1)
|
| 912 |
DX(I) = DX(1)
|
| 913 | |
| 914 |
425 CONTINUE |
| 915 | |
| 916 |
GOTO 500
|
| 917 | |
| 918 |
C --------------- |
| 919 |
C FLOW IN BOUNDARY |
| 920 |
C --------------- |
| 921 | |
| 922 |
430 CONTINUE |
| 923 | |
| 924 |
STOP 'BNDRY: INFLOW BOUNDARY MUST BE SUPPLIED BY THE USER'
|
| 925 | |
| 926 |
GOTO 500
|
| 927 | |
| 928 |
C -------------- |
| 929 |
C PERIODIC BOUNDARY |
| 930 |
C -------------- |
| 931 | |
| 932 |
440 CONTINUE |
| 933 | |
| 934 |
DO 445 I=-4,0
|
| 935 | |
| 936 |
RHO(I) = RHO(NX+I)
|
| 937 |
VEL(I) = VEL(NX+I)
|
| 938 |
U(I) = U(NX+I)
|
| 939 |
P(I) = P(NX+I)
|
| 940 |
CS(I) = CS(NX+I)
|
| 941 |
H(I) = H(NX+I)
|
| 942 |
W(I) = W(NX+I)
|
| 943 |
DX(I) = DX(NX+I)
|
| 944 | |
| 945 |
445 CONTINUE |
| 946 | |
| 947 |
GOTO 500
|
| 948 | |
| 949 |
C --------------------------------------------------------- |
| 950 |
C SPECIAL BOUNDARY (ADD ANY NONSTANDARD BOUNDARY CONDITION HERE) |
| 951 |
C INFLOW JET BOUNDARY |
| 952 |
C --------------------------------------------------------- |
| 953 | |
| 954 |
450 CONTINUE |
| 955 | |
| 956 |
STOP 'BNDRY: NON STANDARD BOUNDARY. TO BE SUPPLIED BY THE USER'
|
| 957 |
|
| 958 |
500 CONTINUE |
| 959 | |
| 960 |
DO 505 I=0,-4,-1
|
| 961 | |
| 962 |
XL(I) = XL(I+1)-DX(I)
|
| 963 |
XR(I) = XR(I+1)-DX(I+1)
|
| 964 |
X(I) = 0.5*(XL(I)+XR(I))
|
| 965 | |
| 966 |
505 CONTINUE |
| 967 | |
| 968 |
C ------------ |
| 969 |
C RIGHT BOUNDARY |
| 970 |
C ------------ |
| 971 | |
| 972 |
GOTO (510, 520, 530, 540, 550), BNDMXX
|
| 973 | |
| 974 |
C ----------------- |
| 975 |
C REFLECTING BOUNDARY |
| 976 |
C ----------------- |
| 977 | |
| 978 |
510 CONTINUE |
| 979 | |
| 980 |
DO 515 I=1,5
|
| 981 | |
| 982 |
RHO(NX+I) = RHO(NX+1-I)
|
| 983 |
VEL(NX+I) = -VEL(NX+1-I)
|
| 984 |
U(NX+I) = U(NX+1-I)
|
| 985 |
P(NX+I) = P(NX+1-I)
|
| 986 |
CS(NX+I) = CS(NX+1-I)
|
| 987 |
H(NX+I) = H(NX+1-I)
|
| 988 |
W(NX+I) = W(NX+1-I)
|
| 989 |
DX(NX+I) = DX(NX+1-I)
|
| 990 | |
| 991 |
515 CONTINUE |
| 992 | |
| 993 |
GOTO 600
|
| 994 | |
| 995 |
C -------------- |
| 996 |
C FLOW OUT BOUNDARY |
| 997 |
C -------------- |
| 998 | |
| 999 |
520 CONTINUE |
| 1000 | |
| 1001 |
DO 525 I=NX+1,NX+5
|
| 1002 | |
| 1003 |
RHO(I) = RHO(NX)
|
| 1004 |
VEL(I) = VEL(NX)
|
| 1005 |
U(I) = U(NX)
|
| 1006 |
P(I) = P(NX)
|
| 1007 |
CS(I) = CS(NX)
|
| 1008 |
H(I) = H(NX)
|
| 1009 |
W(I) = W(NX)
|
| 1010 |
DX(I) = DX(NX)
|
| 1011 | |
| 1012 |
525 CONTINUE |
| 1013 | |
| 1014 |
GOTO 600
|
| 1015 | |
| 1016 |
C -------------- |
| 1017 |
C FLOW IN BOUNDARY |
| 1018 |
C -------------- |
| 1019 | |
| 1020 |
530 CONTINUE |
| 1021 | |
| 1022 |
STOP 'BNDRY: INFLOW BOUNDARY MUST BE SUPPLIED BY THE USER'
|
| 1023 | |
| 1024 |
GOTO 600
|
| 1025 | |
| 1026 |
C --------------- |
| 1027 |
C PERIODIC BOUNDARY |
| 1028 |
C --------------- |
| 1029 | |
| 1030 |
540 CONTINUE |
| 1031 | |
| 1032 |
DO 545 I=1,5
|
| 1033 | |
| 1034 |
RHO(NX+I) = RHO(I)
|
| 1035 |
VEL(NX+I) = VEL(I)
|
| 1036 |
U(NX+I) = U(I)
|
| 1037 |
P(NX+I) = P(I)
|
| 1038 |
CS(NX+I) = CS(I)
|
| 1039 |
H(NX+I) = H(I)
|
| 1040 |
W(NX+I) = W(I)
|
| 1041 |
DX(NX+I) = DX(I)
|
| 1042 | |
| 1043 |
545 CONTINUE |
| 1044 | |
| 1045 |
GOTO 600
|
| 1046 | |
| 1047 |
C --------------------------------------- |
| 1048 |
C SPECIAL BOUNDARY |
| 1049 |
C ADD ANY NONSTANDARD BOUNDARY CONDITION HERE |
| 1050 |
C --------------------------------------- |
| 1051 | |
| 1052 |
550 CONTINUE |
| 1053 | |
| 1054 |
DO 555 I=NX+1,NX+5
|
| 1055 | |
| 1056 |
DX(I) = DX(NX)
|
| 1057 |
XL(I) = XL(I-1) + DX(I-1)
|
| 1058 |
XR(I) = XR(I-1) + DX(I)
|
| 1059 |
X(I) = 0.5*(XL(I)+XR(I))
|
| 1060 |
RHO(I) = 1.D0+DABS(VEL(NX))*TIME/X(I)
|
| 1061 |
VEL(I) = VEL(NX)
|
| 1062 |
U(I) = U(NX)
|
| 1063 |
P(I) = P(NX)
|
| 1064 |
CS(I) = CS(NX)
|
| 1065 |
H(I) = H(NX)
|
| 1066 |
W(I) = W(NX)
|
| 1067 | |
| 1068 |
555 CONTINUE |
| 1069 | |
| 1070 |
600 CONTINUE |
| 1071 | |
| 1072 |
DO 650 I=NX+1,NX+5
|
| 1073 | |
| 1074 |
XL(I) = XL(I-1) + DX(I-1)
|
| 1075 |
XR(I) = XR(I-1) + DX(I)
|
| 1076 |
X(I) = 0.5*(XL(I)+XR(I))
|
| 1077 | |
| 1078 |
650 CONTINUE |
| 1079 | |
| 1080 |
RETURN
|
| 1081 |
END
|
| 1082 | |
| 1083 |
C -------- |
| 1084 |
CN NAME: H Y D R O W |
| 1085 |
C -------- |
| 1086 | |
| 1087 |
CP PURPOSE: |
| 1088 |
CP ADVANCE IN TIME THE 1D EQUATIONS OF RELATIVISTIC HYDRODYNAMICS |
| 1089 |
CP (IN CONSERVATION FORM) IN PLANAR COORDINATES. |
| 1090 |
C |
| 1091 | |
| 1092 |
CC COMMENTS: |
| 1093 |
CC NONE |
| 1094 | |
| 1095 |
SUBROUTINE HYDROW
|
| 1096 | |
| 1097 |
IMPLICIT NONE
|
| 1098 | |
| 1099 |
INCLUDE 'size'
|
| 1100 | |
| 1101 |
C --------- |
| 1102 |
C COMMON BLOCKS |
| 1103 |
C --------- |
| 1104 | |
| 1105 |
INTEGER NEND,NOUT,ITSTP,NX
|
| 1106 |
COMMON /INPTI/ NEND,NOUT,ITSTP,NX
|
| 1107 | |
| 1108 |
DOUBLEPRECISION COEFF1(-4:MN5),COEFF2(-4:MN5),COEFF3(-4:MN5),
|
| 1109 |
& COEFF4(-4:MN5),COEFF5(-4:MN5) |
| 1110 |
COMMON /COEFF/ COEFF1,COEFF2,COEFF3,COEFF4,COEFF5
|
| 1111 | |
| 1112 |
DOUBLEPRECISION DELP(-4:MN5),DELRHO(-4:MN5),DELVEL(-4:MN5),
|
| 1113 |
& DELU(-4:MN5) |
| 1114 |
COMMON /DELU/ DELP,DELRHO,DELVEL,DELU
|
| 1115 | |
| 1116 |
DOUBLEPRECISION FICT(-4:MN5)
|
| 1117 |
COMMON /FICT/ FICT
|
| 1118 | |
| 1119 |
DOUBLEPRECISION FLATN(-4:MN5),FLATN1(-4:MN5)
|
| 1120 |
COMMON /FLAT/ FLATN,FLATN1
|
| 1121 | |
| 1122 |
DOUBLEPRECISION GAMMA
|
| 1123 |
COMMON /ADIND/ GAMMA
|
| 1124 |
|
| 1125 |
DOUBLEPRECISION X(-4:MN5),XL(-4:MN5),XR(-4:MN5),DX(-4:MN5)
|
| 1126 |
COMMON /GRD/ X,XL,XR,DX
|
| 1127 | |
| 1128 |
DOUBLEPRECISION P(-4:MN5),RHO(-4:MN5),VEL(-4:MN5),
|
| 1129 |
& W(-4:MN5),U(-4:MN5),CS(-4:MN5),H(-4:MN5), |
| 1130 |
& DPDRH(-4:MN5),DPDU(-4:MN5),R(-4:MN5),M(-4:MN5), |
| 1131 |
& E(-4:MN5) |
| 1132 |
COMMON /HYDRO/ P,RHO,VEL,W,U,CS,H,DPDRH,DPDU,R,M,E
|
| 1133 | |
| 1134 |
DOUBLEPRECISION TMAX,TOUT,CFL,DTINI,SMALL,SMLRHO,SMALLP,
|
| 1135 |
& SMALLU,GRIDLX,EPSILN,ETA1,ETA2,EPSLN,AK0,OMG1,OMG2 |
| 1136 |
COMMON /INPTF/ TMAX,TOUT,CFL,DTINI,SMALL,SMLRHO,SMALLP,
|
| 1137 |
& SMALLU,GRIDLX,EPSILN,ETA1,ETA2,EPSLN,AK0,OMG1,OMG2 |
| 1138 | |
| 1139 |
DOUBLEPRECISION PL(-4:MN6),PR(-4:MN6),RHOL(-4:MN6),RHOR(-4:MN6),
|
| 1140 |
& VELL(-4:MN6),VELR(-4:MN6), |
| 1141 |
& UL(-4:MN6),UR(-4:MN6),CSL(-4:MN6), |
| 1142 |
& CSR(-4:MN6),RL(-4:MN6),RR(-4:MN6),ML(-4:MN6), |
| 1143 |
& MR(-4:MN6),EL(-4:MN6), |
| 1144 |
& ER(-4:MN6) |
| 1145 |
COMMON /INTERF/ PL,PR,RHOL,RHOR,VELL,VELR,UL,UR,CSL,
|
| 1146 |
& CSR,RL,RR,ML,MR,EL,ER |
| 1147 | |
| 1148 |
DOUBLEPRECISION TIME,DT
|
| 1149 |
COMMON /ZEIT/ TIME,DT
|
| 1150 | |
| 1151 |
DOUBLEPRECISION DP(-4:MN5),P6(-4:MN5),DRHO(-4:MN5),RHO6(-4:MN5),
|
| 1152 |
& DVEL(-4:MN5),VEL6(-4:MN5), |
| 1153 |
& DU(-4:MN5),U6(-4:MN5) |
| 1154 |
COMMON /U6/ DP,P6,DRHO,RHO6,DVEL,VEL6,DU,U6
|
| 1155 | |
| 1156 |
DOUBLEPRECISION PM(-4:MN5),PP(-4:MN5),RHOM(-4:MN5),RHOP(-4:MN5),
|
| 1157 |
& VELM(-4:MN5),VELP(-4:MN5), |
| 1158 |
& UM(-4:MN5),UP(-4:MN5) |
| 1159 |
COMMON /UMP/ PM,PP,RHOM,RHOP,VELM,VELP,UM,UP
|
| 1160 | |
| 1161 |
C ------------ |
| 1162 |
C INTERNAL VARIABLES |
| 1163 |
C ------------ |
| 1164 | |
| 1165 |
INTEGER I
|
| 1166 | |
| 1167 |
DOUBLEPRECISION AUX1
|
| 1168 | |
| 1169 |
DOUBLEPRECISION DTDX(-4:MN5)
|
| 1170 | |
| 1171 |
DOUBLEPRECISION RFLX(-4:MN6),MFLX(-4:MN6),EFLX(-4:MN6)
|
| 1172 | |
| 1173 |
C ------------- |
| 1174 |
C SPATIAL RECONSTRUCTION (PPM) |
| 1175 |
C ------------- |
| 1176 | |
| 1177 |
CALL COEF(NX,COEFF1,COEFF2,COEFF3,COEFF4,COEFF5)
|
| 1178 | |
| 1179 |
CALL INTERP(NX,PM,P,PP,DELP)
|
| 1180 | |
| 1181 |
CALL INTERP(NX,RHOM,RHO,RHOP,DELRHO)
|
| 1182 | |
| 1183 |
CALL DETECT(NX,RHOM,RHO,RHOP,DELRHO)
|
| 1184 | |
| 1185 |
CALL INTERP(NX,VELM,VEL,VELP,DELVEL)
|
| 1186 | |
| 1187 |
CALL FLATEN
|
| 1188 | |
| 1189 | |
| 1190 |
DO 17 I=0,NX+1
|
| 1191 |
RHOM(I) = FLATN(I)*RHO(I) + FLATN1(I)*RHOM(I)
|
| 1192 |
RHOP(I) = FLATN(I)*RHO(I) + FLATN1(I)*RHOP(I)
|
| 1193 |
VELM(I) = FLATN(I)*VEL(I) + FLATN1(I)*VELM(I)
|
| 1194 |
VELP(I) = FLATN(I)*VEL(I) + FLATN1(I)*VELP(I)
|
| 1195 |
PM(I) = FLATN(I)*P(I) + FLATN1(I)*PM(I)
|
| 1196 |
PP(I) = FLATN(I)*P(I) + FLATN1(I)*PP(I)
|
| 1197 |
17 CONTINUE |
| 1198 | |
| 1199 |
CALL MONOT(NX,PM,P,PP,DP,P6)
|
| 1200 | |
| 1201 |
CALL MONOT(NX,RHOM,RHO,RHOP,DRHO,RHO6)
|
| 1202 | |
| 1203 |
CALL MONOT(NX,VELM,VEL,VELP,DVEL,VEL6)
|
| 1204 | |
| 1205 |
C ------------------- |
| 1206 |
C AVERAGED STATES FOR TIME ADVANCE |
| 1207 |
C ------------------- |
| 1208 | |
| 1209 |
CALL STAT1D
|
| 1210 | |
| 1211 |
C ---------------- |
| 1212 |
C COMPUTATION OF NUMERICAL FLUXES (WITH AN EXACT RIEMANN SOLVER) |
| 1213 |
C ---------------- |
| 1214 | |
| 1215 |
DO 23 I=1,NX+1
|
| 1216 | |
| 1217 |
CALL NFLUX(RHOL(I),RHOR(I),PL(I),PR(I),VELL(I),VELR(I),
|
| 1218 |
& UL(I),UR(I),CSL(I),CSR(I),RFLX(I),MFLX(I),EFLX(I)) |
| 1219 |
23 CONTINUE |
| 1220 |
|
| 1221 |
C ---------- |
| 1222 |
C TIME ADVANCE |
| 1223 |
C ---------- |
| 1224 | |
| 1225 |
DO 50 I=1,NX
|
| 1226 |
DTDX(I) = DT/DX(I)
|
| 1227 |
R(I) = R(I) - DTDX(I)*(RFLX(I+1) - RFLX(I))
|
| 1228 |
R(I) = DMAX1(SMLRHO,R(I))
|
| 1229 |
50 CONTINUE |
| 1230 | |
| 1231 |
DO 60 I=1,NX
|
| 1232 |
AUX1 = -DTDX(I)*(MFLX(I+1) - MFLX(I))
|
| 1233 |
M(I) = M(I) + AUX1 + DT*FICT(I)
|
| 1234 |
AUX1 = -DTDX(I)*(EFLX(I+1) - EFLX(I))
|
| 1235 |
E(I) = E(I) + AUX1
|
| 1236 |
60 CONTINUE |
| 1237 | |
| 1238 |
C -------------- |
| 1239 |
C PRIMITIVE VARIABLES |
| 1240 |
C -------------- |
| 1241 | |
| 1242 |
CALL GETPRFQ(NX,R,M,E,VEL,W,RHO,U,P,H,CS,DPDRH,DPDU)
|
| 1243 | |
| 1244 |
RETURN
|
| 1245 |
END
|
| 1246 | |
| 1247 |
C -------- |
| 1248 |
CN NAME: P L T O U T |
| 1249 |
C -------- |
| 1250 | |
| 1251 |
CP PURPOSE: |
| 1252 |
CP COMPUTES THE ANALYTICAL SOLUTION OF STANDARD 1D PROBLEMS AND WRITES |
| 1253 |
CP THE RESULTS IN THE OUTPUT FILES |
| 1254 |
C |
| 1255 | |
| 1256 |
CC COMMENTS: |
| 1257 |
CC NONE |
| 1258 | |
| 1259 |
SUBROUTINE PLTOUT
|
| 1260 | |
| 1261 |
IMPLICIT NONE
|
| 1262 | |
| 1263 |
INCLUDE 'size'
|
| 1264 | |
| 1265 |
C ----------- |
| 1266 |
C COMMON BLOCKS |
| 1267 |
C ----------- |
| 1268 | |
| 1269 |
INTEGER NSTEP
|
| 1270 |
COMMON /NSTEP/ NSTEP
|
| 1271 | |
| 1272 |
INTEGER NOUT1
|
| 1273 |
COMMON /OUTI/ NOUT1
|
| 1274 | |
| 1275 |
INTEGER NEND,NOUT,ITSTP,NX
|
| 1276 |
COMMON /INPTI/ NEND,NOUT,ITSTP,NX
|
| 1277 | |
| 1278 |
DOUBLEPRECISION P(-4:MN5),RHO(-4:MN5),VEL(-4:MN5),W(-4:MN5),
|
| 1279 |
& U(-4:MN5),CS(-4:MN5),H(-4:MN5),DPDRH(-4:MN5), |
| 1280 |
& DPDU(-4:MN5),R(-4:MN5),M(-4:MN5),E(-4:MN5) |
| 1281 |
COMMON /HYDRO/ P,RHO,VEL,W,U,CS,H,DPDRH,DPDU,R,M,E
|
| 1282 | |
| 1283 |
DOUBLEPRECISION X(-4:MN5),XL(-4:MN5),XR(-4:MN5),DX(-4:MN5)
|
| 1284 |
COMMON /GRD/ X,XL,XR,DX
|
| 1285 | |
| 1286 |
DOUBLEPRECISION TOUT1
|
| 1287 |
COMMON /OUTF/ TOUT1
|
| 1288 | |
| 1289 |
DOUBLEPRECISION TIME,DT
|
| 1290 |
COMMON /ZEIT/ TIME,DT
|
| 1291 | |
| 1292 |
DOUBLEPRECISION G
|
| 1293 |
COMMON /ADIND/ G
|
| 1294 | |
| 1295 |
CHARACTER*7 OUTFIL
|
| 1296 |
CHARACTER*8 LABEL
|
| 1297 |
CHARACTER*4 BASENM
|
| 1298 |
CHARACTER*2 SUFFIX
|
| 1299 |
COMMON /CHRC/ LABEL,OUTFIL,BASENM,SUFFIX
|
| 1300 | |
| 1301 |
C ------------ |
| 1302 |
C INTERNAL VARIABLES |
| 1303 |
C ------------ |
| 1304 | |
| 1305 |
INTEGER I
|
| 1306 | |
| 1307 |
DOUBLEPRECISION P1,RHO1,VEL1,U1,CS1
|
| 1308 | |
| 1309 |
DOUBLEPRECISION OCS2,CS2,FCS2,DFDCS2,CS9
|
| 1310 | |
| 1311 |
DOUBLEPRECISION P2,RHO2,VEL2,U2
|
| 1312 | |
| 1313 |
DOUBLEPRECISION P3,RHO3,VEL3,U3,CS3
|
| 1314 | |
| 1315 |
DOUBLEPRECISION P4,RHO4,VEL4,U4,CS4
|
| 1316 | |
| 1317 |
DOUBLEPRECISION P5,RHO5,VEL5,U5,CS5
|
| 1318 | |
| 1319 |
DOUBLEPRECISION P6,RHO6,VEL6,U6,CS6
|
| 1320 | |
| 1321 |
DOUBLEPRECISION P7,RHO7,VEL7,U7,CS7
|
| 1322 | |
| 1323 |
DOUBLEPRECISION P8,RHO8,VEL8,U8,CS8
|
| 1324 | |
| 1325 |
DOUBLEPRECISION P10,RHO10,VEL10,U10,CS10
|
| 1326 | |
| 1327 |
DOUBLEPRECISION X1,X2,X3,X4,X5,X6,X7,X8,X9
|
| 1328 | |
| 1329 |
DOUBLEPRECISION A,B,C,D,K,L
|
| 1330 | |
| 1331 |
DOUBLEPRECISION PA(MN),RHOA(MN),VELA(MN),UA(MN)
|
| 1332 | |
| 1333 |
DOUBLEPRECISION WW,VS,XS
|
| 1334 | |
| 1335 |
C ---------------------- |
| 1336 |
C ANALYTICAL SOLUTION FOR STANDARD TESTS |
| 1337 |
C ---------------------- |
| 1338 | |
| 1339 |
IF (BASENM.EQ.'RSR_') THEN
|
| 1340 | |
| 1341 |
WW = 1.D0/SQRT(1.D0 - VEL(1)*VEL(1))
|
| 1342 |
U1 = 0.D0
|
| 1343 |
U2 = WW - 1.D0
|
| 1344 |
RHO1 = 1.D0
|
| 1345 |
RHO2 = ((G + 1.D0)/(G - 1.D0) + G*U2/(G - 1.D0))*RHO1
|
| 1346 |
VEL1 = VEL(1)
|
| 1347 |
VEL2 = 0.D0
|
| 1348 |
P1 = (G - 1.D0)*RHO1*U1
|
| 1349 |
P2 = (G - 1.D0)*RHO2*U2
|
| 1350 |
VS = -VEL1/(RHO2/RHO1/WW - 1.D0)
|
| 1351 |
XS = XR(NX) + VS*TIME
|
| 1352 |
|
| 1353 |
DO 30 I = 1,NX
|
| 1354 | |
| 1355 |
IF (X(I).LT.XS) THEN
|
| 1356 |
UA(I) = U1
|
| 1357 |
RHOA(I) = RHO1
|
| 1358 |
VELA(I) = VEL1
|
| 1359 |
PA(I) = P1
|
| 1360 |
ELSE
|
| 1361 |
UA(I) = U2
|
| 1362 |
RHOA(I) = RHO2
|
| 1363 |
VELA(I) = VEL2
|
| 1364 |
PA(I) = P2
|
| 1365 |
END IF
|
| 1366 | |
| 1367 |
30 CONTINUE |
| 1368 | |
| 1369 |
END IF
|
| 1370 | |
| 1371 |
IF (BASENM.EQ.'RST_') THEN
|
| 1372 |
|
| 1373 |
P1 = 1.D0
|
| 1374 |
RHO1 = 1.D0
|
| 1375 |
VEL1 = 0.D0
|
| 1376 |
U1 = P1/(G - 1.D0)/RHO1
|
| 1377 |
CS1 = DSQRT(G*P1*(G - 1.D0)/(RHO1*(G - 1.D0) + G*P1))
|
| 1378 | |
| 1379 |
P3 = 0.3115D0
|
| 1380 |
RHO3 = 0.4345D0
|
| 1381 |
VEL3 = 0.4262D0
|
| 1382 |
U3 = P3/(G - 1.D0)/RHO3
|
| 1383 |
CS3 = DSQRT(G*P3*(G - 1.D0)/(RHO3*(G - 1.D0) + G*P3))
|
| 1384 | |
| 1385 |
P4 = P3
|
| 1386 |
RHO4 = 0.273D0
|
| 1387 |
VEL4 = VEL3
|
| 1388 |
U4 = P4/(G - 1.D0)/RHO4
|
| 1389 |
CS4 = DSQRT(G*P4*(G - 1.D0)/(RHO4*(G - 1.D0) + G*P4))
|
| 1390 | |
| 1391 |
P5 = 0.1D0
|
| 1392 |
RHO5 = 0.125D0
|
| 1393 |
VEL5 = 0.D0
|
| 1394 |
U5 = P5/(G - 1.D0)/RHO5
|
| 1395 |
CS5 = DSQRT(G*P5*(G - 1.D0)/(RHO5*(G - 1.D0) + G*P5))
|
| 1396 | |
| 1397 |
X1 = 0.5D0 + (VEL1 - CS1)*TIME/(1.D0 - VEL1*CS1)
|
| 1398 | |
| 1399 |
X2 = 0.5D0 + (VEL3 - CS3)*TIME/(1.D0 - VEL3*CS3)
|
| 1400 | |
| 1401 |
X3 = 0.5D0 + VEL3*TIME
|
| 1402 | |
| 1403 |
X4 = 0.5D0 + VEL4*TIME/(1.D0 - RHO5*DSQRT(1.D0 - VEL4**2)/RHO4)
|
| 1404 | |
| 1405 |
ELSE IF(BASENM.EQ.'RBW_') THEN
|
| 1406 | |
| 1407 |
P1 = 1000.D0
|
| 1408 |
RHO1 = 1.D0
|
| 1409 |
VEL1 = 0.D0
|
| 1410 |
U1 = P1/(G-1.D0)/RHO1
|
| 1411 |
CS1 = DSQRT(G*P1*(G - 1.D0)/(RHO1*(G - 1.D0) + G*P1))
|
| 1412 | |
| 1413 |
P3 = 18.6D0
|
| 1414 |
RHO3 = 9.15D-2
|
| 1415 |
VEL3 = 0.960D0
|
| 1416 |
U3 = P3/(G-1.D0)/RHO3
|
| 1417 |
CS3 = DSQRT(G*P3*(G - 1.D0)/(RHO3*(G - 1.D0) + G*P3))
|
| 1418 | |
| 1419 |
P4 = P3
|
| 1420 |
RHO4 = 10.75D0
|
| 1421 |
VEL4 = VEL3
|
| 1422 |
U4 = P4/(G - 1.D0)/RHO4
|
| 1423 |
CS4 = DSQRT(G*P4*(G - 1.D0)/(RHO4*(G - 1.D0) + G*P4))
|
| 1424 | |
| 1425 |
P5 = 1.D-2
|
| 1426 |
RHO5 = 1.D0
|
| 1427 |
VEL5 = 0.D0
|
| 1428 |
U5 = P5/(G - 1.D0)/RHO5
|
| 1429 |
CS5 = DSQRT(G*P5*(G - 1.D0)/(RHO5*(G - 1.D0) + G*P5))
|
| 1430 | |
| 1431 |
X1 = 0.5D0 + (VEL1 - CS1)*TIME/(1.D0 - VEL1*CS1)
|
| 1432 | |
| 1433 |
X2 = 0.5D0 + (VEL3 - CS3)*TIME/(1.D0 - VEL3*CS3)
|
| 1434 | |
| 1435 |
X3 = 0.5D0 + VEL3*TIME
|
| 1436 | |
| 1437 |
X4 = 0.5D0 + VEL4*TIME/(1.D0 - RHO5*DSQRT(1.D0 - VEL4**2)/RHO4)
|
| 1438 | |
| 1439 |
ELSE IF(BASENM.EQ.'SCHN') THEN
|
| 1440 | |
| 1441 |
P1 = 13.33333333D0
|
| 1442 |
RHO1 = 10.D0
|
| 1443 |
VEL1 = 0.D0
|
| 1444 |
U1 = P1/(G - 1.D0)/RHO1
|
| 1445 |
CS1 = DSQRT(G*P1*(G - 1.D0)/(RHO1*(G - 1.D0) + G*P1))
|
| 1446 | |
| 1447 |
P3 = 1.448D0
|
| 1448 |
RHO3 = 2.639D0
|
| 1449 |
VEL3 = 0.714D0
|
| 1450 |
U3 = P3/(G - 1.D0)/RHO3
|
| 1451 |
CS3 = DSQRT(G*P3*(G - 1.D0)/(RHO3*(G - 1.D0) + G*P3))
|
| 1452 | |
| 1453 |
P4 = P3
|
| 1454 |
RHO4 = 5.071D0
|
| 1455 |
VEL4 = VEL3
|
| 1456 |
U4 = P4/(G - 1.D0)/RHO4
|
| 1457 |
CS4 = DSQRT(G*P4*(G - 1.D0)/(RHO4*(G - 1.D0)+G*P4))
|
| 1458 | |
| 1459 |
P5 = 0.666666666666D-6
|
| 1460 |
RHO5 = 1.D0
|
| 1461 |
VEL5 = 0.D0
|
| 1462 |
U5 = P5/(G - 1.D0)/RHO5
|
| 1463 |
CS5 = DSQRT(G*P5*(G - 1.D0)/(RHO5*(G - 1.D0) + G*P5))
|
| 1464 | |
| 1465 |
X1 = 0.5D0 + (VEL1 - CS1)*TIME/(1.D0 - VEL1*CS1)
|
| 1466 | |
| 1467 |
X2 = 0.5D0 + (VEL3 - CS3)*TIME/(1.D0 - VEL3*CS3)
|
| 1468 | |
| 1469 |
X3 = 0.5D0 + VEL3*TIME
|
| 1470 | |
| 1471 |
X4 = 0.5D0 + VEL4*TIME/(1.D0 - RHO5*DSQRT(1.D0 - VEL4**2)/RHO4)
|
| 1472 | |
| 1473 |
ELSE IF (BASENM.EQ.'RBWI') THEN
|
| 1474 | |
| 1475 |
U1 = 2.5D3
|
| 1476 |
RHO1 = 1.D0
|
| 1477 |
VEL1 = 0.D0
|
| 1478 |
P1 = (G - 1.D0)*U1*RHO1
|
| 1479 |
CS1 = DSQRT(G*P1*(G - 1.D0)/(RHO1*(G - 1.D0) + G*P1))
|
| 1480 |
|
| 1481 |
RHO3 = 0.0491D0
|
| 1482 |
VEL3 = 0.957D0
|
| 1483 |
P3 = 14.71D0
|
| 1484 |
U3 = P3/(G - 1.D0)/RHO3
|
| 1485 |
CS3 = DSQRT(G*P3*(G - 1.D0)/(RHO3*(G - 1.D0) + G*P3))
|
| 1486 |
|
| 1487 |
RHO4 = 14.39D0
|
| 1488 |
VEL4 = VEL3
|
| 1489 |
P4 = P3
|
| 1490 |
U4 = P4/(G - 1.D0)/RHO4
|
| 1491 |
CS4 = DSQRT(G*P4*(G - 1.D0)/(RHO4*(G - 1.D0) + G*P4))
|
| 1492 |
|
| 1493 |
IF (TIME.LT.0.4200) THEN
|
| 1494 | |
| 1495 |
U5 = 2.5D-2
|
| 1496 |
RHO5 = 1.D0
|
| 1497 |
VEL5 = 0.D0
|
| 1498 |
P5 = (G - 1.D0)*RHO5*U5
|
| 1499 |
CS5 = DSQRT(G*P5*(G - 1.D0)/(RHO5*(G - 1.D0) + G*P5))
|
| 1500 |
|
| 1501 |
U6 = U5
|
| 1502 |
RHO6 = RHO5
|
| 1503 |
VEL6 = VEL5
|
| 1504 |
P6 = P5
|
| 1505 |
CS6 = CS5
|
| 1506 | |
| 1507 |
ELSE
|
| 1508 | |
| 1509 |
RHO5 = 104.41D0
|
| 1510 |
VEL5 = 0.456D0
|
| 1511 |
P5 = 369.84D0
|
| 1512 |
U5 = P5/(G - 1.D0)/RHO5
|
| 1513 |
CS5 = DSQRT(G*P5*(G - 1.D0)/(RHO5*(G - 1.D0) + G*P5))
|
| 1514 |
|
| 1515 |
RHO6 = 117.25D0
|
| 1516 |
VEL6 = VEL5
|
| 1517 |
P6 = P5
|
| 1518 |
U6 = P6/(G - 1.D0)/RHO6
|
| 1519 |
CS6 = DSQRT(G*P6*(G - 1.D0)/(RHO6*(G - 1.D0) + G*P6))
|
| 1520 | |
| 1521 |
END IF
|
| 1522 | |
| 1523 |
RHO7 = 9.72D0
|
| 1524 |
VEL7 = -0.882D0
|
| 1525 |
P7 = 4.639D0
|
| 1526 |
U7 = P7/(G - 1.D0)/RHO7
|
| 1527 |
CS7 = DSQRT(G*P7*(G - 1.D0)/(RHO7*(G - 1.D0) + G*P7))
|
| 1528 |
|
| 1529 |
RHO8 = 0.112D0
|
| 1530 |
VEL8 = VEL7
|
| 1531 |
P8 = P7
|
| 1532 |
U8 = P8/(G - 1.D0)/RHO8
|
| 1533 |
CS8 = DSQRT(G*P8*(G - 1.D0)/(RHO8*(G - 1.D0) + G*P8))
|
| 1534 |
|
| 1535 |
U10 = 2.5D2
|
| 1536 |
RHO10= 1.D0
|
| 1537 |
VEL10= 0.D0
|
| 1538 |
P10 = (G - 1.D0)*U10*RHO10
|
| 1539 |
CS10 = DSQRT(G*P10*(G - 1.D0)/(RHO10*(G - 1.D0) + G*P10))
|
| 1540 | |
| 1541 |
X1 = 0.1D0 - TIME*CS1
|
| 1542 |
|
| 1543 |
X2 = 0.1D0 + TIME*(VEL3 - CS3)/(1.D0 - VEL3*CS3)
|
| 1544 |
|
| 1545 |
X3 = 0.1D0 + TIME*VEL3
|
| 1546 |
|
| 1547 |
IF (TIME.LT.0.4200D0) THEN
|
| 1548 |
X4 = 0.1D0 + TIME*0.9776D0
|
| 1549 |
|
| 1550 |
X5 = 0.9D0 - TIME*0.9274D0
|
| 1551 |
|
| 1552 |
X6 = X5
|
| 1553 |
ELSE
|
| 1554 |
X4 = 0.5106D0 + (TIME - 0.4200D0)*0.088D0
|
| 1555 |
|
| 1556 |
X5 = 0.5106D0 + (TIME - 0.4200D0)*VEL5
|
| 1557 |
|
| 1558 |
X6 = 0.5106D0 + (TIME - 0.4200D0)*0.703D0
|
| 1559 |
END IF
|
| 1560 |
|
| 1561 |
X7 = 0.9D0 + TIME*VEL7
|
| 1562 |
|
| 1563 |
X8 = 0.9D0 + TIME*(VEL8 + CS8)/(1.D0 + VEL8*CS8)
|
| 1564 |
|
| 1565 |
X9 = 0.9D0 + TIME*CS10
|
| 1566 | |
| 1567 |
END IF
|
| 1568 | |
| 1569 |
IF (BASENM.EQ.'RST_'.OR.BASENM.EQ.'RBW_'.OR.
|
| 1570 |
& BASENM.EQ.'SCHN') THEN |
| 1571 | |
| 1572 |
DO 70 I=1,NX
|
| 1573 | |
| 1574 |
IF (X(I).LT.X1) THEN
|
| 1575 | |
| 1576 |
PA(I) = P1
|
| 1577 |
RHOA(I) = RHO1
|
| 1578 |
VELA(I) = VEL1
|
| 1579 |
UA(I) = U1
|
| 1580 |
|
| 1581 |
ELSE IF (X(I).LT.X2) THEN
|
| 1582 |
|
| 1583 |
A = (X(I) - 0.5D0)/TIME
|
| 1584 |
B = DSQRT(G - 1.D0)
|
| 1585 |
C = (B + CS1)/(B - CS1)
|
| 1586 |
D = -B/2.D0
|
| 1587 |
K = (1.D0 + A)/(1.D0 - A)
|
| 1588 |
L = C*K**D
|
| 1589 |
OCS2 = CS1
|
| 1590 |
50 FCS2 = L*(1.D0 + OCS2)**D*(OCS2 - B) + |
| 1591 |
& (1.D0 - OCS2)**D*(OCS2+B) |
| 1592 |
DFDCS2 = L*(1.D0 + OCS2)**D*(1.D0 + D*(OCS2 - B)/
|
| 1593 |
& (1.D0 + OCS2)) + |
| 1594 |
& (1.D0 - OCS2)**D*(1.D0 - D*(OCS2 + B)/ |
| 1595 |
& (1.D0 - OCS2)) |
| 1596 |
CS2 = OCS2 - FCS2/DFDCS2
|
| 1597 |
|
| 1598 |
IF (DABS(CS2 - OCS2)/OCS2.GT.5.D-10) THEN
|
| 1599 |
OCS2 = CS2
|
| 1600 |
GOTO 50
|
| 1601 |
END IF
|
| 1602 |
|
| 1603 |
VELA(I) = (A + CS2)/(1.D0 + A*CS2)
|
| 1604 |
RHOA(I) = RHO1*((CS2**2*(G - 1.D0 - CS1**2))/
|
| 1605 |
& (CS1**2*(G - 1.D0 - CS2**2.)))**(1.D0/(G - 1.D0)) |
| 1606 |
PA(I) = CS2**2*(G - 1.D0)*RHOA(I)/(G - 1.D0 - CS2**2)/G
|
| 1607 |
UA(I) = PA(I)/(G - 1.D0)/RHOA(I)
|
| 1608 |
|
| 1609 |
ELSE IF (X(I).LT.X3) THEN
|
| 1610 | |
| 1611 |
PA(I) = P3
|
| 1612 |
RHOA(I) = RHO3
|
| 1613 |
VELA(I) = VEL3
|
| 1614 |
UA(I) = U3
|
| 1615 | |
| 1616 |
ELSE IF (X(I).LT.X4) THEN
|
| 1617 |
|
| 1618 |
PA(I) = P4
|
| 1619 |
RHOA(I) = RHO4
|
| 1620 |
VELA(I) = VEL4
|
| 1621 |
UA(I) = U4
|
| 1622 |
|
| 1623 |
ELSE
|
| 1624 |
|
| 1625 |
PA(I) = P5
|
| 1626 |
RHOA(I) = RHO5
|
| 1627 |
VELA(I) = VEL5
|
| 1628 |
UA(I) = U5
|
| 1629 |
END IF
|
| 1630 | |
| 1631 |
70 CONTINUE |
| 1632 | |
| 1633 |
END IF
|
| 1634 | |
| 1635 |
IF (BASENM.EQ.'RBWI') THEN
|
| 1636 | |
| 1637 |
DO 80 I=1,NX
|
| 1638 |
|
| 1639 |
IF (X(I).LT.X1) THEN
|
| 1640 | |
| 1641 |
RHOA(I) = RHO1
|
| 1642 |
VELA(I) = VEL1
|
| 1643 |
PA(I) = P1
|
| 1644 |
|
| 1645 |
ELSE IF (X(I).LT.X2) THEN
|
| 1646 | |
| 1647 |
A = (X(I) - 0.1D0)/TIME
|
| 1648 |
B = DSQRT(G - 1.D0)
|
| 1649 |
C = (B + CS1)/(B - CS1)
|
| 1650 |
D = -B/2.D0
|
| 1651 |
K = (1.D0 + A)/(1.D0 - A)
|
| 1652 |
L = C*K**D
|
| 1653 |
OCS2 = CS1
|
| 1654 |
52 FCS2 = L*(1.D0 + OCS2)**D*(OCS2 - B) + |
| 1655 |
& (1.D0 - OCS2)**D*(OCS2 + B) |
| 1656 |
DFDCS2 = L*(1.D0 + OCS2)**D*(1.D0 + D*(OCS2 - B)/
|
| 1657 |
& (1.D0 + OCS2)) + |
| 1658 |
& (1.D0 - OCS2)**D*(1.D0 - D*(OCS2 + B)/ |
| 1659 |
& (1.D0 - OCS2)) |
| 1660 |
CS2 = OCS2 - FCS2/DFDCS2
|
| 1661 |
|
| 1662 |
IF (ABS(CS2-OCS2)/OCS2.GT.5.E-10)THEN
|
| 1663 |
OCS2 = CS2
|
| 1664 |
GOTO 52
|
| 1665 |
END IF
|
| 1666 | |
| 1667 |
VELA(I) = (A+CS2)/(1.D0+A*CS2)
|
| 1668 |
RHOA(I) = RHO1*((CS2**2.*(G-1.D0-CS1**2))/
|
| 1669 |
& (CS1**2*(G-1.D0-CS2**2)))**(1.D0/(G-1.D0)) |
| 1670 |
PA(I) = CS2**2*(G-1.D0)*RHOA(I)/(G-1.D0-CS2**2)/G
|
| 1671 |
UA(I) = PA(I)/(G-1.D0)/RHOA(I)
|
| 1672 | |
| 1673 |
ELSE IF (X(I).LT.X3) THEN
|
| 1674 | |
| 1675 |
RHOA(I) = RHO3
|
| 1676 |
VELA(I) = VEL3
|
| 1677 |
PA(I) = P3
|
| 1678 | |
| 1679 |
ELSE IF (X(I).LT.X4) THEN
|
| 1680 | |
| 1681 |
RHOA(I) = RHO4
|
| 1682 |
VELA(I) = VEL4
|
| 1683 |
PA(I) = P4
|
| 1684 | |
| 1685 |
ELSE IF (X(I).LT.X5) THEN
|
| 1686 | |
| 1687 |
RHOA(I) = RHO5
|
| 1688 |
VELA(I) = VEL5
|
| 1689 |
PA(I) = P5
|
| 1690 | |
| 1691 |
ELSE IF (X(I).LT.X6) THEN
|
| 1692 | |
| 1693 |
RHOA(I) = RHO6
|
| 1694 |
VELA(I) = VEL6
|
| 1695 |
PA(I) = P6
|
| 1696 | |
| 1697 |
ELSE IF (X(I).LT.X7) THEN
|
| 1698 | |
| 1699 |
RHOA(I) = RHO7
|
| 1700 |
VELA(I) = VEL7
|
| 1701 |
PA(I) = P7
|
| 1702 | |
| 1703 |
ELSE IF (X(I).LT.X8) THEN
|
| 1704 | |
| 1705 |
RHOA(I) = RHO8
|
| 1706 |
VELA(I) = VEL8
|
| 1707 |
PA(I) = P8
|
| 1708 |
|
| 1709 |
ELSE IF (X(I).LT.X9) THEN
|
| 1710 |
|
| 1711 |
A = (X(I) - 0.9D0)/TIME
|
| 1712 |
B = SQRT(G - 1.D0)
|
| 1713 |
C = (B + CS10)/(B - CS10)
|
| 1714 |
D = B/2.D0
|
| 1715 |
K = (1.D0 + A)/(1.D0 - A)
|
| 1716 |
L = C*K**D
|
| 1717 |
OCS2 = CS10
|
| 1718 |
54 FCS2 = L*(1.D0 - OCS2)**D*(OCS2 - B) + |
| 1719 |
& (1.D0 + OCS2)**D*(OCS2 + B) |
| 1720 |
DFDCS2 = L*(1.D0 - OCS2)**D*(1.D0 + D*(OCS2 - B)/
|
| 1721 |
& (1.D0 - OCS2))+ |
| 1722 |
& (1.D0 + OCS2)**D*(1.D0 - D*(OCS2 + B)/ |
| 1723 |
& (1.D0 + OCS2)) |
| 1724 |
CS9 = OCS2 - FCS2/DFDCS2
|
| 1725 |
|
| 1726 |
IF (DABS(CS9-OCS2)/OCS2.GT.5.D-10)THEN
|
| 1727 |
OCS2 = CS9
|
| 1728 |
GOTO 54
|
| 1729 |
END IF
|
| 1730 |
|
| 1731 |
VELA(I) = (A - CS9)/(1.D0 - A*CS9)
|
| 1732 |
RHOA(I) = RHO10*((CS9 **2*(G - 1.D0 - CS10**2))/
|
| 1733 |
& (CS10**2*(G - 1.D0 - CS9 **2)))**(1.D0/(G - 1.D0)) |
| 1734 |
PA(I) = CS9**2*(G - 1.D0)*RHOA(I)/(G - 1.D0 - CS9**2)/G
|
| 1735 |
UA(I) = PA(I)/(G - 1.D0)/RHOA(I)
|
| 1736 | |
| 1737 |
ELSE
|
| 1738 |
|
| 1739 |
RHOA(I) = RHO10
|
| 1740 |
VELA(I) = VEL10
|
| 1741 |
PA(I) = P10
|
| 1742 | |
| 1743 |
END IF
|
| 1744 | |
| 1745 |
80 CONTINUE |
| 1746 |
|
| 1747 |
END IF
|
| 1748 | |
| 1749 |
C ---- |
| 1750 |
C OUTPUT |
| 1751 |
C ---- |
| 1752 | |
| 1753 |
OPEN(10,FILE='DATA/'//OUTFIL,FORM='FORMATTED',STATUS='NEW')
|
| 1754 |
WRITE(10,111) NSTEP,TIME
|
| 1755 |
111 FORMAT('N =', I6, 3X, 'TIME = ', 1PE10.3)
|
| 1756 | |
| 1757 |
DO 85 I=1,NX
|
| 1758 |
WRITE(10,200) X(I),P(I),PA(I),RHO(I),RHOA(I),
|
| 1759 |
& VEL(I),VELA(I) |
| 1760 |
85 CONTINUE |
| 1761 | |
| 1762 |
200 FORMAT(F6.4,1X,2(F11.4,1X),2(F9.4,1X),2(F7.5,1X)) |
| 1763 |
CLOSE(10)
|
| 1764 | |
| 1765 |
NOUT1 = 0
|
| 1766 |
TOUT1 = 0.D0
|
| 1767 | |
| 1768 |
CALL FILNAM
|
| 1769 | |
| 1770 |
RETURN
|
| 1771 |
END
|
| 1772 | |
| 1773 |
C -------- |
| 1774 |
CN NAME: E O S |
| 1775 |
C -------- |
| 1776 | |
| 1777 |
CP PURPOSE: |
| 1778 |
CP COMPUTES DERIVED THERMODYNAMICAL QUANTITIES |
| 1779 |
C |
| 1780 | |
| 1781 |
CC COMMENTS: |
| 1782 |
CC GAMMA-LAW EOS |
| 1783 | |
| 1784 |
SUBROUTINE EOS(N,RHO,U,G,P,H,CS,DPDRH,DPDU)
|
| 1785 | |
| 1786 |
IMPLICIT NONE
|
| 1787 | |
| 1788 |
INCLUDE 'size'
|
| 1789 | |
| 1790 |
C ------- |
| 1791 |
C ARGUMENTS |
| 1792 |
C ------- |
| 1793 | |
| 1794 |
INTEGER N
|
| 1795 | |
| 1796 |
DOUBLEPRECISION U(-4:MN5),RHO(-4:MN5),P(-4:MN5),H(-4:MN5),
|
| 1797 |
& CS(-4:MN5),DPDRH(-4:MN5),DPDU(-4:MN5) |
| 1798 |
|
| 1799 |
DOUBLEPRECISION G
|
| 1800 | |
| 1801 |
C ----------- |
| 1802 |
C INTERNAL VARIABLES |
| 1803 |
C ----------- |
| 1804 | |
| 1805 |
INTEGER I
|
| 1806 | |
| 1807 |
DOUBLEPRECISION GAM1
|
| 1808 | |
| 1809 |
DO 10 I=1,N
|
| 1810 |
GAM1 = G -1.D0
|
| 1811 |
P(I) = GAM1*RHO(I)*U(I)
|
| 1812 |
DPDRH(I) = GAM1*U(I)
|
| 1813 |
DPDU(I) = GAM1*RHO(I)
|
| 1814 |
H(I) = 1.D0 + U(I) + P(I)/RHO(I)
|
| 1815 |
CS(I) = DSQRT((DPDRH(I) + P(I)*DPDU(I)/RHO(I)/RHO(I))/H(I))
|
| 1816 |
10 CONTINUE |
| 1817 | |
| 1818 |
RETURN
|
| 1819 |
END
|
| 1820 | |
| 1821 |
C -------- |
| 1822 |
CN NAME: C O E F |
| 1823 |
C -------- |
| 1824 | |
| 1825 |
CP PURPOSE: |
| 1826 |
CP COMPUTES THE COEFFICIENTS FOR INTERPOLATED VALUES |
| 1827 |
C |
| 1828 | |
| 1829 |
CC COMMENTS: |
| 1830 |
CC COMPUTES DE GRID-DEPENDENT COEFFICIENTS APPEARING IN EQS.59-61 OF MARTI |
| 1831 |
CC AND MUELLER (1996), JCP, VOL. 123, 1-14 |
| 1832 | |
| 1833 |
SUBROUTINE COEF(N,COEFF1,COEFF2,COEFF3,COEFF4,COEFF5)
|
| 1834 | |
| 1835 |
IMPLICIT NONE
|
| 1836 | |
| 1837 |
INCLUDE 'size'
|
| 1838 | |
| 1839 |
C -------- |
| 1840 |
C ARGUMENTS |
| 1841 |
C -------- |
| 1842 | |
| 1843 |
INTEGER N
|
| 1844 | |
| 1845 |
DOUBLEPRECISION COEFF1(-4:MN5),COEFF2(-4:MN5),COEFF3(-4:MN5)
|
| 1846 |
DOUBLEPRECISION COEFF4(-4:MN5),COEFF5(-4:MN5)
|
| 1847 | |
| 1848 |
C ---------- |
| 1849 |
C COMMON BLOCKS |
| 1850 |
C ---------- |
| 1851 | |
| 1852 |
DOUBLEPRECISION X(-4:MN5),XL(-4:MN5),XR(-4:MN5),DX(-4:MN5)
|
| 1853 |
COMMON /GRD/ X,XL,XR,DX
|
| 1854 | |
| 1855 |
C -------------- |
| 1856 |
C INTERNAL VARIABLES |
| 1857 |
C -------------- |
| 1858 |
|
| 1859 |
INTEGER I
|
| 1860 | |
| 1861 |
DOUBLEPRECISION SCRCH1(-4:MN6),SCRCH2(-4:MN6),SCRCH3(-4:MN6),
|
| 1862 |
& SCRCH4(-4:MN6) |
| 1863 | |
| 1864 | |
| 1865 |
DO 10 I=0,N+2
|
| 1866 | |
| 1867 |
SCRCH1(I) = DX(I) + DX(I-1)
|
| 1868 |
SCRCH2(I) = SCRCH1(I) + DX(I)
|
| 1869 |
SCRCH3(I) = SCRCH1(I) + DX(I-1)
|
| 1870 | |
| 1871 |
10 CONTINUE |
| 1872 | |
| 1873 |
DO 20 I=0,N+1
|
| 1874 | |
| 1875 |
SCRCH4(I) = DX(I)/(SCRCH1(I) + DX(I+1))
|
| 1876 |
COEFF1(I) = SCRCH4(I)*SCRCH3(I)/SCRCH1(I+1)
|
| 1877 |
COEFF2(I) = SCRCH4(I)*SCRCH2(I+1)/SCRCH1(I)
|
| 1878 | |
| 1879 |
20 CONTINUE |
| 1880 | |
| 1881 |
DO 30 I=0,N
|
| 1882 |
|
| 1883 |
SCRCH4(I) = 1.D0/(SCRCH1(I) + SCRCH1(I+2))
|
| 1884 |
COEFF3(I) = -SCRCH4(I)*DX(I)*SCRCH1(I)/SCRCH3(I+1)
|
| 1885 |
COEFF4(I) = SCRCH4(I)*DX(I+1)*SCRCH1(I+2)/SCRCH2(I+1)
|
| 1886 |
COEFF5(I) = DX(I) - 2.D0*(DX(I+1)*COEFF3(I) + DX(I)*COEFF4(I))
|
| 1887 |
COEFF5(I) = COEFF5(I)/SCRCH1(I+1)
|
| 1888 | |
| 1889 |
30 CONTINUE |
| 1890 |
|
| 1891 |
RETURN
|
| 1892 |
END
|
| 1893 | |
| 1894 |
C -------- |
| 1895 |
CN NAME: I N T E R P |
| 1896 |
C -------- |
| 1897 | |
| 1898 |
CP PURPOSE: |
| 1899 |
CP COMPUTES INTERPOLATED VALUES AT INTERFACES |
| 1900 |
C |
| 1901 | |
| 1902 |
CC COMMENTS: |
| 1903 |
CC STEP 1 IN THE RECONSTRUCTION PROCEDURE (SEE APPENDIX I IN MARTI |
| 1904 |
CC & MUELLER 1996) |
| 1905 | |
| 1906 |
SUBROUTINE INTERP(N,UM,U,UP,DELU)
|
| 1907 | |
| 1908 |
IMPLICIT NONE
|
| 1909 | |
| 1910 |
INCLUDE 'size'
|
| 1911 | |
| 1912 |
C -------- |
| 1913 |
C ARGUMENTS |
| 1914 |
C -------- |
| 1915 | |
| 1916 |
INTEGER N
|
| 1917 | |
| 1918 |
DOUBLEPRECISION UM(-4:MN5),U(-4:MN5),UP(-4:MN5),DELU(-4:MN5)
|
| 1919 | |
| 1920 |
C --------- |
| 1921 |
C COMMON BLOCKS |
| 1922 |
C --------- |
| 1923 | |
| 1924 |
DOUBLEPRECISION COEFF1(-4:MN5),COEFF2(-4:MN5),COEFF3(-4:MN5)
|
| 1925 |
DOUBLEPRECISION COEFF4(-4:MN5),COEFF5(-4:MN5)
|
| 1926 |
COMMON /COEFF/ COEFF1,COEFF2,COEFF3,COEFF4,COEFF5
|
| 1927 | |
| 1928 |
C ----------- |
| 1929 |
C INTERNAL VARIABLES |
| 1930 |
C ----------- |
| 1931 | |
| 1932 |
INTEGER I
|
| 1933 | |
| 1934 |
DOUBLEPRECISION SCRCH1(-4:MN6),SCRCH2(-4:MN6)
|
| 1935 | |
| 1936 |
DOUBLEPRECISION SDELU
|
| 1937 | |
| 1938 |
DO 10 I=-2,N+3
|
| 1939 | |
| 1940 |
SCRCH1(I) = U(I) - U(I-1)
|
| 1941 | |
| 1942 |
10 CONTINUE |
| 1943 | |
| 1944 |
C ------------------------------------------------------ |
| 1945 |
C DELU(I) AS IN EQ.61 OF MARTI AND MUELLER (1996), JCP, VOL. 123, 1-14 |
| 1946 |
C ------------------------------------------------------ |
| 1947 | |
| 1948 |
DO 20 I=0,N+1
|
| 1949 | |
| 1950 |
DELU(I) = COEFF1(I)*SCRCH1(I+1) + COEFF2(I)*SCRCH1(I)
|
| 1951 | |
| 1952 |
20 CONTINUE |
| 1953 | |
| 1954 |
C ------------------------------------------------------- |
| 1955 |
C DELU(I) AS IN EQ.60 OF MARTI AND MUELLER (1996), JCP, VOL. 123, 1-14 |
| 1956 |
C ------------------------------------------------------- |
| 1957 | |
| 1958 |
DO 30 I=0,N+1
|
| 1959 | |
| 1960 |
IF (SCRCH1(I+1)*SCRCH1(I).GT.0.D0) THEN
|
| 1961 |
SDELU = DELU(I)/DABS(DELU(I))
|
| 1962 |
SCRCH2(I) = MIN(DABS(SCRCH1(I)),DABS(SCRCH1(I+1)))
|
| 1963 |
DELU(I) = MIN(DABS(DELU(I)),2.D0*SCRCH2(I))*SDELU
|
| 1964 |
ELSE
|
| 1965 |
DELU(I) = 0.D0
|
| 1966 |
END IF
|
| 1967 | |
| 1968 |
30 CONTINUE |
| 1969 | |
| 1970 |
C ---------------------------------------------- |
| 1971 |
C INTERFACE VALUES AS IN EQ.59 OF MARTI AND MUELLER (1996), JCP, |
| 1972 |
C VOL. 123, 1-14 |
| 1973 |
C ---------------------------------------------- |
| 1974 | |
| 1975 |
DO 40 I=0,N
|
| 1976 | |
| 1977 |
UP(I) = U(I) + COEFF5(I)*SCRCH1(I+1) + COEFF3(I)*DELU(I+1)
|
| 1978 |
UP(I) = UP(I) + COEFF4(I)*DELU(I)
|
| 1979 |
UM(I+1) = UP(I)
|
| 1980 | |
| 1981 |
40 CONTINUE |
| 1982 | |
| 1983 |
RETURN
|
| 1984 |
END
|
| 1985 | |
| 1986 |
C -------- |
| 1987 |
CN NAME: D E T E C T |
| 1988 |
C -------- |
| 1989 | |
| 1990 |
CP PURPOSE: |
| 1991 |
CP DETECTS CONTACT DISCONTINUITIES AND STEEPENS THE CORRESPONDING |
| 1992 |
CP RECONSTRUCTED VALUES AT INTERFACES |
| 1993 |
C |
| 1994 | |
| 1995 |
CC COMMENTS: |
| 1996 |
CC STEP 2 IN THE RECONSTRUCTION PROCEDURE (SEE APPENDIX I IN MARTI |
| 1997 |
CC & MUELLER 1996) |
| 1998 | |
| 1999 |
SUBROUTINE DETECT(N,UM,U,UP,DELU)
|
| 2000 | |
| 2001 |
IMPLICIT NONE
|
| 2002 | |
| 2003 |
INCLUDE 'size'
|
| 2004 | |
| 2005 |
C ------- |
| 2006 |
C ARGUMENTS |
| 2007 |
C ------- |
| 2008 | |
| 2009 |
INTEGER N
|
| 2010 | |
| 2011 |
DOUBLEPRECISION UM(-4:MN5),U(-4:MN5),UP(-4:MN5),DELU(-4:MN5)
|
| 2012 | |
| 2013 |
C ----------- |
| 2014 |
C COMMON BLOCKS |
| 2015 |
C ----------- |
| 2016 | |
| 2017 |
DOUBLEPRECISION X(-4:MN5),XL(-4:MN5),XR(-4:MN5),DX(-4:MN5)
|
| 2018 |
COMMON /GRD/ X,XL,XR,DX
|
| 2019 | |
| 2020 |
DOUBLEPRECISION P(-4:MN5),RHO(-4:MN5),VEL(-4:MN5),W(-4:MN5),
|
| 2021 |
& UU(-4:MN5),CS(-4:MN5),H(-4:MN5),DPDRH(-4:MN5), |
| 2022 |
& DPDU(-4:MN5),R(-4:MN5),M(-4:MN5),E(-4:MN5) |
| 2023 |
COMMON /HYDRO/ P,RHO,VEL,W,UU,CS,H,DPDRH,DPDU,R,M,E
|
| 2024 | |
| 2025 |
DOUBLEPRECISION TMAX,TOUT,CFL,DTINI,SMALL,SMLRHO,SMALLP,SMALLU,
|
| 2026 |
& GRIDLX,EPSILN,ETA1,ETA2,EPSLN,AK0,OMG1,OMG2 |
| 2027 |
COMMON /INPTF/ TMAX,TOUT,CFL,DTINI,SMALL,SMLRHO,SMALLP,SMALLU,
|
| 2028 |
& GRIDLX,EPSILN,ETA1,ETA2,EPSLN,AK0,OMG1,OMG2 |
| 2029 | |
| 2030 |
DOUBLEPRECISION GB
|
| 2031 |
COMMON /ADIND/ GB
|
| 2032 | |
| 2033 |
C --------- |
| 2034 |
C INTERNAL VARIABLES |
| 2035 |
C --------- |
| 2036 | |
| 2037 |
INTEGER I
|
| 2038 | |
| 2039 |
DOUBLEPRECISION D2U(-4:MN6),ETA(-4:MN6),ETATIL(-4:MN6)
|
| 2040 |
|
| 2041 |
DOUBLEPRECISION SCRCH1(-4:MN6),SCRCH2(-4:MN6),SCRCH3(-4:MN6),
|
| 2042 |
& SCRCH4(-4:MN6) |
| 2043 | |
| 2044 | |
| 2045 |
DO 10 I=-1,N+3
|
| 2046 | |
| 2047 |
SCRCH1(I) = DX(I) + DX(I-1)
|
| 2048 |
SCRCH2(I) = SCRCH1(I) + DX(I+1)
|
| 2049 |
SCRCH3(I) = U(I) - U(I-1)
|
| 2050 |
SCRCH1(I) = SCRCH3(I)/SCRCH1(I)
|
| 2051 | |
| 2052 |
10 CONTINUE |
| 2053 | |
| 2054 |
DO 20 I=-1,N+2
|
| 2055 |
|
| 2056 |
D2U(I) = (SCRCH1(I+1) - SCRCH1(I))/SCRCH2(I)
|
| 2057 |
SCRCH4(I) = X(I) - X(I-1)
|
| 2058 |
SCRCH4(I) = SCRCH4(I)*SCRCH4(I)*SCRCH4(I)
|
| 2059 | |
| 2060 |
20 CONTINUE |
| 2061 | |
| 2062 |
DO 30 I=0,N+1
|
| 2063 | |
| 2064 |
SCRCH1(I) = D2U(I+1)*D2U(I-1)
|
| 2065 |
SCRCH3(I) = DABS(U(I+1) - U(I-1))
|
| 2066 |
SCRCH3(I) = SCRCH3(I) - EPSLN*MIN(DABS(U(I+1)),DABS(U(I-1)))
|
| 2067 | |
| 2068 |
30 CONTINUE |
| 2069 | |
| 2070 |
C ------------------------------------------------------ |
| 2071 |
C ETATIL(I) AS IN EQ.67 OF MARTI AND MUELLER (1996), JCP, VOL. 123, 1-14 |
| 2072 |
C ------------------------------------------------------- |
| 2073 | |
| 2074 |
DO 40 I=0,N+1
|
| 2075 |
|
| 2076 |
IF ((U(I+1) - U(I-1)).EQ.0.D0) THEN
|
| 2077 |
SCRCH2(I) = SMALL*SMLRHO
|
| 2078 |
ELSE
|
| 2079 |
SCRCH2(I) = U(I+1) - U(I-1)
|
| 2080 |
END IF
|
| 2081 | |
| 2082 |
IF ((SCRCH1(I).GT.0.D0).OR.(SCRCH3(I).LT.0.D0)) THEN
|
| 2083 |
ETATIL(I) = 0.D0
|
| 2084 |
ELSE
|
| 2085 |
ETATIL(I) = (D2U(I-1) - D2U(I+1))*(SCRCH4(I) + SCRCH4(I+1))
|
| 2086 |
ETATIL(I) = ETATIL(I)/(X(I+1) - X(I-1))/SCRCH2(I)
|
| 2087 |
END IF
|
| 2088 | |
| 2089 |
40 CONTINUE |
| 2090 | |
| 2091 |
C ------------------------------------------------------- |
| 2092 |
C ETA(I) AS IN EQ.66 OF MARTI AND MUELLER (1996), JCP, VOL. 123, 1-14 |
| 2093 |
C ONLY FOR ZONES VERIFYING EQ.63 (OTHERWISE, ZERO) |
| 2094 |
C ------------------------------------------------------- |
| 2095 | |
| 2096 |
DO 50 I=0,N+1
|
| 2097 | |
| 2098 |
ETA(I) = MAX(0.D0,MIN(ETA1*(ETATIL(I) - ETA2),1.D0))
|
| 2099 |
SCRCH1(I) = DABS(P (I+1) - P (I-1))/MIN(P (I+1),P (I-1))
|
| 2100 |
SCRCH2(I) = DABS(RHO(I+1) - RHO(I-1))/MIN(RHO(I+1),RHO(I-1))
|
| 2101 | |
| 2102 |
50 CONTINUE |
| 2103 | |
| 2104 |
DO 60 I=0,N+1
|
| 2105 | |
| 2106 |
IF (GB*AK0*SCRCH2(I).LT.SCRCH1(I)) THEN
|
| 2107 |
ETA(I) = 0.D0
|
| 2108 |
END IF
|
| 2109 | |
| 2110 |
60 CONTINUE |
| 2111 | |
| 2112 |
C ---------------------------- |
| 2113 |
C NEW RECONSTRUCTED VALUES (EQ.65) |
| 2114 |
C ---------------------------- |
| 2115 | |
| 2116 |
DO 70 I=0,N+1
|
| 2117 | |
| 2118 |
SCRCH1(I) = U(I-1) + 0.5D0*DELU(I-1)
|
| 2119 |
SCRCH2(I) = U(I+1) - 0.5D0*DELU(I+1)
|
| 2120 |
UM(I) = UM(I)*(1.D0-ETA(I)) + SCRCH1(I)*ETA(I)
|
| 2121 |
UP(I) = UP(I)*(1.D0-ETA(I)) + SCRCH2(I)*ETA(I)
|
| 2122 | |
| 2123 |
70 CONTINUE |
| 2124 | |
| 2125 |
RETURN
|
| 2126 |
END
|
| 2127 | |
| 2128 |
C -------- |
| 2129 |
CN NAME: M O N O T |
| 2130 |
C -------- |
| 2131 | |
| 2132 |
CP PURPOSE: |
| 2133 |
CP RECONSTRUCTED VALUES OBTAINED IN STEPS 1 TO 3 ARE MODIFIED SUCH THAT |
| 2134 |
CP THE INTERPOLATION PARABOLA IN EACH ZONE IS MONOTONE |
| 2135 |
C |
| 2136 | |
| 2137 |
CC COMMENTS: |
| 2138 |
CC STEP 4 IN THE RECONSTRUCTION PROCEDURE (SEE APPENDIX I IN MARTI |
| 2139 |
CC & MUELLER 1996) |
| 2140 | |
| 2141 |
SUBROUTINE MONOT(N,UM,U,UP,DU,U6)
|
| 2142 | |
| 2143 |
IMPLICIT NONE
|
| 2144 | |
| 2145 |
INCLUDE 'size'
|
| 2146 | |
| 2147 |
C -------- |
| 2148 |
C ARGUMENTS |
| 2149 |
C -------- |
| 2150 | |
| 2151 |
INTEGER N
|
| 2152 | |
| 2153 |
DOUBLEPRECISION UM(-4:MN5),U(-4:MN5),UP(-4:MN5),DU(-4:MN5)
|
| 2154 |
DOUBLEPRECISION U6(-4:MN5)
|
| 2155 | |
| 2156 |
C -------- |
| 2157 |
C INTERNAL VARIABLES |
| 2158 |
C -------- |
| 2159 | |
| 2160 |
INTEGER I
|
| 2161 | |
| 2162 |
DOUBLEPRECISION SCRCH1(-4:MN6),SCRCH2(-4:MN6),SCRCH3(-4:MN6)
|
| 2163 |
|
| 2164 |
C ----------------------------------------------------- |
| 2165 |
C NEW RECONSRUCTED VALUES IF CONDITION IN EQ.73 OF MARTI & MUELLER |
| 2166 |
C 1996 HOLDS |
| 2167 |
C ----------------------------------------------------- |
| 2168 | |
| 2169 |
DO 10 I=0,N+1
|
| 2170 | |
| 2171 |
DU(I) = UP(I) - UM(I)
|
| 2172 |
SCRCH1(I) = UP(I) - U(I)
|
| 2173 |
SCRCH1(I) = SCRCH1(I)*(UM(I)-U(I))
|
| 2174 | |
| 2175 |
10 CONTINUE |
| 2176 | |
| 2177 |
DO 20 I=0,N+1
|
| 2178 | |
| 2179 |
IF (SCRCH1(I).GE.0.D0) THEN
|
| 2180 |
UM(I) = U(I)
|
| 2181 |
UP(I) = U(I)
|
| 2182 |
END IF
|
| 2183 | |
| 2184 |
20 CONTINUE |
| 2185 | |
| 2186 |
C -------------------------------------------------------- |
| 2187 |
C NEW RECONSTRUCTED VALUES IF CONDITION IN EQ.74 OR EQ.75 OF MARTI |
| 2188 |
C & MUELLER 1996 HOLDS |
| 2189 |
C -------------------------------------------------------- |
| 2190 | |
| 2191 |
DO 30 I=0,N+1
|
| 2192 | |
| 2193 |
DU(I) = UP(I) - UM(I)
|
| 2194 |
SCRCH1(I) = (UP(I) - U(I))*(UM(I) - U(I))
|
| 2195 | |
| 2196 |
IF (SCRCH1(I).EQ.0.D0) THEN
|
| 2197 |
SCRCH2(I) = UM(I)
|
| 2198 |
SCRCH3(I) = UP(I)
|
| 2199 |
ELSE
|
| 2200 |
SCRCH2(I) = 3.D0*U(I) - 2.D0*UP(I)
|
| 2201 |
SCRCH3(I) = 3.D0*U(I) - 2.D0*UM(I)
|
| 2202 |
END IF
|
| 2203 | |
| 2204 |
30 CONTINUE |
| 2205 | |
| 2206 |
DO 40 I=0,N+1
|
| 2207 | |
| 2208 |
IF (DU(I)*(UM(I) - SCRCH2(I)).LT.0.D0) THEN
|
| 2209 |
UM(I) = SCRCH2(I)
|
| 2210 |
END IF
|
| 2211 | |
| 2212 |
IF (DU(I)*(SCRCH3(I) - UP(I)).LT.0.D0) THEN
|
| 2213 |
UP(I) = SCRCH3(I)
|
| 2214 |
END IF
|
| 2215 | |
| 2216 |
40 CONTINUE |
| 2217 | |
| 2218 |
C ------------------------------------------- |
| 2219 |
C COMPUTATION OF AUXILIAR VARIABLES FOR TIME ADVANCE |
| 2220 |
C ------------------------------------------- |
| 2221 | |
| 2222 |
DO 50 I=0,N+1
|
| 2223 | |
| 2224 |
DU(I) = UP(I) - UM(I)
|
| 2225 |
U6(I) = 6.D0*U(I) - 3.D0*(UM(I) + UP(I))
|
| 2226 | |
| 2227 |
50 CONTINUE |
| 2228 | |
| 2229 |
RETURN
|
| 2230 |
END
|
| 2231 | |
| 2232 |
C -------- |
| 2233 |
CN NAME: F L A T E N |
| 2234 |
C -------- |
| 2235 | |
| 2236 |
CP PURPOSE: |
| 2237 |
CP THIS SUBROUTINE FLATTENS ZONE STRUCTURE IN REGIONS WHERE SHOCKS |
| 2238 |
CP ARE TOO THIN |
| 2239 |
C |
| 2240 | |
| 2241 |
CC COMMENTS: |
| 2242 |
CC STEP 3 IN THE RECONSTRUCTION PROCEDURE (SEE APPENDIX I IN MARTI |
| 2243 |
CC & MUELLER 1996) |
| 2244 | |
| 2245 |
SUBROUTINE FLATEN
|
| 2246 | |
| 2247 |
IMPLICIT NONE
|
| 2248 | |
| 2249 |
INCLUDE 'size'
|
| 2250 | |
| 2251 |
C ------------- |
| 2252 |
C COMMON BLOCKS |
| 2253 |
C ------------- |
| 2254 | |
| 2255 |
INTEGER NEND,NOUT,ITSTP,NX
|
| 2256 |
COMMON /INPTI/ NEND,NOUT,ITSTP,NX
|
| 2257 | |
| 2258 |
DOUBLEPRECISION FLATN(-4:MN5),FLATN1(-4:MN5)
|
| 2259 |
COMMON /FLAT/ FLATN,FLATN1
|
| 2260 | |
| 2261 |
DOUBLEPRECISION P(-4:MN5),RHO(-4:MN5),VEL(-4:MN5),W(-4:MN5),
|
| 2262 |
& U(-4:MN5),CS(-4:MN5),H(-4:MN5),DPDRH(-4:MN5), |
| 2263 |
& DPDU(-4:MN5),R(-4:MN5),M(-4:MN5),E(-4:MN5) |
| 2264 |
COMMON /HYDRO/ P,RHO,VEL,W,U,CS,H,DPDRH,DPDU,R,M,E
|
| 2265 | |
| 2266 |
DOUBLEPRECISION TMAX,TOUT,CFL,DTINI,SMALL,SMLRHO,SMALLP,SMALLU,
|
| 2267 |
& GRIDLX,EPSILN,ETA1,ETA2,EPSLN,AK0,OMG1,OMG2 |
| 2268 |
COMMON /INPTF/ TMAX,TOUT,CFL,DTINI,SMALL,SMLRHO,SMALLP,SMALLU,
|
| 2269 |
& GRIDLX,EPSILN,ETA1,ETA2,EPSLN,AK0,OMG1,OMG2 |
| 2270 | |
| 2271 |
C ------------ |
| 2272 |
C INTERNAL VARIABLES |
| 2273 |
C ------------ |
| 2274 | |
| 2275 |
INTEGER I
|
| 2276 | |
| 2277 |
DOUBLEPRECISION SCRCH1(-4:MN6),SCRCH2(-4:MN6),SCRCH3(-4:MN6)
|
| 2278 | |
| 2279 |
DOUBLEPRECISION DP(-4:MN5),DVEL(-4:MN5),DP2
|
| 2280 | |
| 2281 |
DO 20 I=-2,NX+3
|
| 2282 | |
| 2283 |
DP(I) = P(I+1) - P(I-1)
|
| 2284 |
DVEL(I) = VEL(I+1) - VEL(I-1)
|
| 2285 |
SCRCH1(I) = EPSILN*DMIN1(P(I+1),P(I-1)) - DABS(DP(I))
|
| 2286 | |
| 2287 |
IF (SCRCH1(I).LT.0.D0.AND.DVEL(I).LT.0.D0) THEN
|
| 2288 |
SCRCH1(I) = 1.D0
|
| 2289 |
ELSE
|
| 2290 |
SCRCH1(I) = 0.D0
|
| 2291 |
END IF
|
| 2292 | |
| 2293 |
20 CONTINUE |
| 2294 | |
| 2295 |
DO 30 I=-1,NX+2
|
| 2296 | |
| 2297 |
DP2 = P(I+2) - P(I-2)
|
| 2298 | |
| 2299 |
IF (DP2.EQ.0.D0) THEN
|
| 2300 | |
| 2301 |
IF (DP(I).EQ.0.D0) THEN
|
| 2302 |
SCRCH2(I) = -OMG1
|
| 2303 |
ELSE
|
| 2304 |
SCRCH2(I) = 1.D0 - OMG1
|
| 2305 |
END IF
|
| 2306 | |
| 2307 |
ELSE
|
| 2308 |
SCRCH2(I) = DP(I)/DP2 - OMG1
|
| 2309 |
END IF
|
| 2310 | |
| 2311 |
SCRCH3(I) = SCRCH1(I)*DMAX1(0.D0,SCRCH2(I)*OMG2)
|
| 2312 | |
| 2313 |
30 CONTINUE |
| 2314 | |
| 2315 |
DO 40 I=0,NX+1
|
| 2316 | |
| 2317 |
IF (DP(I).LT.0.D0) THEN
|
| 2318 |
SCRCH2(I) = SCRCH3(I+1)
|
| 2319 |
ELSE
|
| 2320 |
SCRCH2(I) = SCRCH3(I-1)
|
| 2321 |
END IF
|
| 2322 | |
| 2323 |
40 CONTINUE |
| 2324 | |
| 2325 |
DO 45 I=0,NX+1
|
| 2326 | |
| 2327 |
FLATN(I) = DMAX1(SCRCH2(I),SCRCH3(I))
|
| 2328 |
FLATN(I) = DMAX1(0.D0,DMIN1(1.D0,FLATN(I)))
|
| 2329 |
FLATN1(I) = 1.D0 - FLATN(I)
|
| 2330 | |
| 2331 |
45 CONTINUE |
| 2332 | |
| 2333 |
RETURN
|
| 2334 |
END
|
| 2335 | |
| 2336 | |
| 2337 |
C -------- |
| 2338 |
CN NAME: S T A T 1 D |
| 2339 |
C -------- |
| 2340 | |
| 2341 |
CP PURPOSE: |
| 2342 |
CP THIS SUBROUTINE CALCULATES EFFECTIVE SECOND-ORDER-ACCURATE LEFT |
| 2343 |
CP AND RIGHT STATES FOR RIEMANN PROBLEMS IN ONE DIMENSIONAL |
| 2344 |
CP CALCULATIONS. |
| 2345 |
C |
| 2346 | |
| 2347 |
CC COMMENTS: |
| 2348 |
CC THIS ROUTINE CLOSELY FOLLOWS THE ANALYTICAL DEVELOPMENTS DESCRIBED IN |
| 2349 |
CC MARTI & MUELLER, JCP, 1996 |
| 2350 | |
| 2351 |
SUBROUTINE STAT1D
|
| 2352 | |
| 2353 |
IMPLICIT NONE
|
| 2354 | |
| 2355 |
INCLUDE 'size'
|
| 2356 | |
| 2357 |
C --------- |
| 2358 |
C COMMON BLOCKS |
| 2359 |
C --------- |
| 2360 | |
| 2361 |
INTEGER NEND,NOUT,ITSTP,NX
|
| 2362 |
COMMON /INPTI/ NEND,NOUT,ITSTP,NX
|
| 2363 | |
| 2364 |
DOUBLEPRECISION TMAX,TOUT,CFL,DTINI,SMALL,SMLRHO,SMALLP,SMALLU,
|
| 2365 |
& GRIDLX,EPSILN,ETA1,ETA2,EPSLN,AK0,OMG1,OMG2 |
| 2366 |
COMMON /INPTF/ TMAX,TOUT,CFL,DTINI,SMALL,SMLRHO,SMALLP,SMALLU,
|
| 2367 |
& GRIDLX,EPSILN,ETA1,ETA2,EPSLN,AK0,OMG1,OMG2 |
| 2368 | |
| 2369 |
DOUBLEPRECISION P(-4:MN5),RHO(-4:MN5),VEL(-4:MN5),W(-4:MN5),
|
| 2370 |
& U(-4:MN5),CS(-4:MN5),H(-4:MN5),DPDRH(-4:MN5), |
| 2371 |
& DPDU(-4:MN5),R(-4:MN5),M(-4:MN5),E(-4:MN5) |
| 2372 |
COMMON /HYDRO/ P,RHO,VEL,W,U,CS,H,DPDRH,DPDU,R,M,E
|
| 2373 | |
| 2374 |
DOUBLEPRECISION PM(-4:MN5),PP(-4:MN5),RHOM(-4:MN5),RHOP(-4:MN5),
|
| 2375 |
& VELM(-4:MN5),VELP(-4:MN5),UM(-4:MN5),UP(-4:MN5) |
| 2376 |
COMMON /UMP/ PM,PP,RHOM,RHOP,VELM,VELP,UM,UP
|
| 2377 | |
| 2378 |
DOUBLEPRECISION DP(-4:MN5),P6(-4:MN5),DRHO(-4:MN5),RHO6(-4:MN5),
|
| 2379 |
& DVEL(-4:MN5),VEL6(-4:MN5),DU(-4:MN5),U6(-4:MN5) |
| 2380 |
COMMON /U6/ DP,P6,DRHO,RHO6,DVEL,VEL6,DU,U6
|
| 2381 | |
| 2382 |
DOUBLEPRECISION PL(-4:MN6),PR(-4:MN6),RHOL(-4:MN6),RHOR(-4:MN6),
|
| 2383 |
& VELL(-4:MN6),VELR(-4:MN6),UL(-4:MN6),UR(-4:MN6), |
| 2384 |
& CSL(-4:MN6),CSR(-4:MN6),RL(-4:MN6),RR(-4:MN6), |
| 2385 |
& ML(-4:MN6),MR(-4:MN6),EL(-4:MN6),ER(-4:MN6) |
| 2386 |
COMMON /INTERF/ PL,PR,RHOL,RHOR,VELL,VELR,UL,UR,CSL,CSR,RL,RR,ML,
|
| 2387 |
& MR,EL,ER |
| 2388 | |
| 2389 |
DOUBLEPRECISION FICT(-4:MN5)
|
| 2390 |
COMMON /FICT/ FICT
|
| 2391 | |
| 2392 |
DOUBLEPRECISION TIME,DT
|
| 2393 |
COMMON /ZEIT/ TIME,DT
|
| 2394 | |
| 2395 |
DOUBLEPRECISION X(-4:MN5),XL(-4:MN5),XR(-4:MN5),DX(-4:MN5)
|
| 2396 |
COMMON /GRD/ X,XL,XR,DX
|
| 2397 | |
| 2398 |
DOUBLEPRECISION GB
|
| 2399 |
COMMON /ADIND/ GB
|
| 2400 | |
| 2401 |
C --------- |
| 2402 |
C INTERNAL VARIABLES |
| 2403 |
C --------- |
| 2404 | |
| 2405 |
INTEGER I
|
| 2406 | |
| 2407 |
DOUBLEPRECISION LAMB1(-4:MN5),LAMB2(-4:MN5),LAMB3(-4:MN5)
|
| 2408 | |
| 2409 |
DOUBLEPRECISION P1L(-4:MN6),P1R(-4:MN6),P2L(-4:MN6),P2R(-4:MN6),
|
| 2410 |
& P3L(-4:MN6),P3R(-4:MN6),RHO1L(-4:MN6), |
| 2411 |
& RHO1R(-4:MN6),RHO2L(-4:MN6),RHO2R(-4:MN6), |
| 2412 |
& RHO3L(-4:MN6),RHO3R(-4:MN6),VEL1L(-4:MN6), |
| 2413 |
& VEL1R(-4:MN6),VEL2L(-4:MN6),VEL2R(-4:MN6), |
| 2414 |
& VEL3L(-4:MN6),VEL3R(-4:MN6) |
| 2415 | |
| 2416 |
DOUBLEPRECISION BETA1L(-4:MN6),BETA2L(-4:MN6),BETA3L(-4:MN6),
|
| 2417 |
& BETA1R(-4:MN6),BETA2R(-4:MN6),BETA3R(-4:MN6) |
| 2418 | |
| 2419 | |
| 2420 |
DOUBLEPRECISION SCRCH1(-4:MN6),SCRCH2(-4:MN6),SCRCH3(-4:MN6),
|
| 2421 |
& SCRCH4(-4:MN6),SCRCH5(-4:MN6) |
| 2422 | |
| 2423 |
DO 10 I=0,NX+1
|
| 2424 | |
| 2425 |
LAMB1(I) = (VEL(I) - CS(I))/(1.D0 - VEL(I)*CS(I))
|
| 2426 |
LAMB2(I) = VEL(I)
|
| 2427 |
LAMB3(I) = (VEL(I) + CS(I))/(1.D0 + VEL(I)*CS(I))
|
| 2428 | |
| 2429 |
10 CONTINUE |
| 2430 | |
| 2431 |
CALL AVRG1D(NX,DT,LAMB1,PM,PP,DP,P6,RHOM,RHOP,DRHO,RHO6,
|
| 2432 |
& VELM,VELP,DVEL,VEL6, |
| 2433 |
& P1L,P1R,RHO1L,RHO1R,VEL1L,VEL1R) |
| 2434 | |
| 2435 |
CALL AVRG1D(NX,DT,LAMB2,PM,PP,DP,P6,RHOM,RHOP,DRHO,RHO6,
|
| 2436 |
& VELM,VELP,DVEL,VEL6, |
| 2437 |
& P2L,P2R,RHO2L,RHO2R,VEL2L,VEL2R) |
| 2438 | |
| 2439 |
CALL AVRG1D(NX,DT,LAMB3,PM,PP,DP,P6,RHOM,RHOP,DRHO,RHO6,
|
| 2440 |
& VELM,VELP,DVEL,VEL6, |
| 2441 |
& P3L,P3R,RHO3L,RHO3R,VEL3L,VEL3R) |
| 2442 | |
| 2443 |
C ------------- |
| 2444 |
C EFFECTIVE LEFT STATES |
| 2445 |
C ------------- |
| 2446 | |
| 2447 |
DO 20 I=1,NX+1
|
| 2448 | |
| 2449 |
SCRCH1(I) = P3L(I)/(GB - 1.D0)/RHO3L(I)
|
| 2450 |
SCRCH1(I) = 1.D0 + SCRCH1(I) + P3L(I)/RHO3L(I)
|
| 2451 |
SCRCH2(I) = DSQRT(GB*P3L(I)/RHO3L(I)/SCRCH1(I))
|
| 2452 |
SCRCH1(I) = SCRCH1(I)*SCRCH2(I)
|
| 2453 |
SCRCH3(I) = 1.D0/(1.D0 - VEL3L(I)**2)
|
| 2454 |
SCRCH3(I) = RHO3L(I)*SCRCH3(I)
|
| 2455 |
SCRCH4(I) = 0.D0
|
| 2456 |
SCRCH5(I) = 0.D0
|
| 2457 | |
| 2458 |
BETA1L(I) = 0.5D0*(VEL3L(I) - VEL1L(I) - (P3L(I) - P1L(I))/
|
| 2459 |
& SCRCH3(I)/SCRCH1(I) - DT*SCRCH4(I)) |
| 2460 |
BETA2L(I) = RHO3L(I) - RHO2L(I) - (P3L(I) - P2L(I))/
|
| 2461 |
& SCRCH1(I)/SCRCH2(I) |
| 2462 |
BETA3L(I) = -0.5D0*DT*SCRCH5(I)
|
| 2463 | |
| 2464 |
20 CONTINUE |
| 2465 | |
| 2466 |
DO 25 I=1,NX+1
|
| 2467 | |
| 2468 |
IF (LAMB3(I-1).LE.0.D0) THEN
|
| 2469 |
BETA3L(I) = 0.D0
|
| 2470 |
END IF
|
| 2471 | |
| 2472 |
IF (LAMB2(I-1).LE.0.D0) THEN
|
| 2473 |
BETA2L(I) = 0.D0
|
| 2474 |
END IF
|
| 2475 | |
| 2476 |
IF (LAMB1(I-1).LE.0.D0) THEN
|
| 2477 |
BETA1L(I) = 0.D0
|
| 2478 |
END IF
|
| 2479 | |
| 2480 |
25 CONTINUE |
| 2481 | |
| 2482 |
DO 30 I=1,NX+1
|
| 2483 |
|
| 2484 |
PL(I) = P3L(I) + SCRCH3(I)*SCRCH1(I)*(BETA1L(I) + BETA3L(I))
|
| 2485 |
PL(I) = DMAX1(SMALLP,PL(I))
|
| 2486 | |
| 2487 |
RHOL(I) = RHO3L(I) + SCRCH3(I)/SCRCH2(I)*(BETA1L(I) +
|
| 2488 |
& BETA3L(I)) - BETA2L(I) |
| 2489 |
RHOL(I) = DMAX1(SMLRHO,RHOL(I))
|
| 2490 | |
| 2491 |
VELL(I) = VEL3L(I) + BETA3L(I) - BETA1L(I)
|
| 2492 | |
| 2493 |
UL(I) = PL(I)/(GB - 1.D0)/RHOL(I)
|
| 2494 | |
| 2495 |
SCRCH1(I) = 1.D0 + UL(I) + PL(I)/RHOL(I)
|
| 2496 | |
| 2497 |
CSL(I) = DSQRT(GB*PL(I)/RHOL(I)/SCRCH1(I))
|
| 2498 | |
| 2499 |
30 CONTINUE |
| 2500 | |
| 2501 |
C ---------- |
| 2502 |
C EFFECTIVE RIGHT STATES |
| 2503 |
C ---------- |
| 2504 | |
| 2505 |
DO 35 I=1,NX+1
|
| 2506 | |
| 2507 |
SCRCH1(I) = P1R(I)/(GB - 1.D0)/RHO1R(I)
|
| 2508 |
SCRCH1(I) = 1.D0 + SCRCH1(I) + P1R(I)/RHO1R(I)
|
| 2509 |
SCRCH2(I) = DSQRT(GB*P1R(I)/RHO1R(I)/SCRCH1(I))
|
| 2510 |
SCRCH1(I) = SCRCH1(I)*SCRCH2(I)
|
| 2511 |
SCRCH3(I) = 1.D0/(1.D0 - VEL1R(I)**2)
|
| 2512 |
SCRCH3(I) = RHO1R(I)*SCRCH3(I)
|
| 2513 |
SCRCH4(I) = 0.D0
|
| 2514 |
SCRCH5(I) = 0.D0
|
| 2515 | |
| 2516 |
BETA1R(I) = -0.5D0*DT*SCRCH4(I)
|
| 2517 |
BETA2R(I) = RHO1R(I) - RHO2R(I) - (P1R(I)-P2R(I))/
|
| 2518 |
& SCRCH1(I)/SCRCH2(I) |
| 2519 |
BETA3R(I) = -0.5D0*(VEL1R(I) - VEL3R(I) + (P1R(I) - P3R(I))/
|
| 2520 |
& SCRCH3(I)/SCRCH1(I) + DT*SCRCH5(I)) |
| 2521 |
35 CONTINUE |
| 2522 | |
| 2523 |
DO 40 I=1,NX+1
|
| 2524 | |
| 2525 |
IF (LAMB3(I).GE.0.D0) THEN
|
| 2526 |
BETA3R(I) = 0.D0
|
| 2527 |
END IF
|
| 2528 | |
| 2529 |
IF (LAMB2(I).GE.0.D0) THEN
|
| 2530 |
BETA2R(I) = 0.D0
|
| 2531 |
END IF
|
| 2532 | |
| 2533 |
IF (LAMB1(I).GE.0.D0) THEN
|
| 2534 |
BETA1R(I) = 0.D0
|
| 2535 |
END IF
|
| 2536 | |
| 2537 |
40 CONTINUE |
| 2538 | |
| 2539 |
DO 45 I=1,NX+1
|
| 2540 | |
| 2541 |
PR(I) = P1R(I) + SCRCH3(I)*SCRCH1(I)*(BETA1R(I) + BETA3R(I))
|
| 2542 |
PR(I) = DMAX1(SMALLP,PR(I))
|
| 2543 | |
| 2544 |
RHOR(I) = RHO1R(I) + SCRCH3(I)/SCRCH2(I)*(BETA1R(I) +
|
| 2545 |
& BETA3R(I)) - BETA2R(I) |
| 2546 |
RHOR(I) = DMAX1(SMLRHO,RHOR(I))
|
| 2547 | |
| 2548 |
VELR(I) = VEL1R(I) + BETA3R(I) - BETA1R(I)
|
| 2549 | |
| 2550 |
UR(I) = PR(I)/(GB - 1.D0)/RHOR(I)
|
| 2551 | |
| 2552 |
SCRCH1(I) = 1.D0 + UR(I) + PR(I)/RHOR(I)
|
| 2553 | |
| 2554 |
CSR(I) = DSQRT(GB*PR(I)/RHOR(I)/SCRCH1(I))
|
| 2555 | |
| 2556 |
45 CONTINUE |
| 2557 | |
| 2558 |
C -------------- |
| 2559 |
C CONSERVED VARIABLES |
| 2560 |
C -------------- |
| 2561 | |
| 2562 |
DO 60 I=1,NX+1
|
| 2563 | |
| 2564 |
SCRCH1(I) = 1.D0/DSQRT(1.D0 - VELL(I)*VELL(I))
|
| 2565 |
SCRCH2(I) = 1.D0 + UL(I) + PL(I)/RHOL(I)
|
| 2566 |
RL(I) = RHOL(I)*SCRCH1(I)
|
| 2567 |
ML(I) = RL(I)*SCRCH2(I)*SCRCH1(I)*VELL(I)
|
| 2568 |
EL(I) = RL(I)*SCRCH2(I)*SCRCH1(I) - PL(I) - RL(I)
|
| 2569 | |
| 2570 |
60 CONTINUE |
| 2571 |
|
| 2572 |
DO 70 I=1,NX+1
|
| 2573 | |
| 2574 |
SCRCH1(I) = 1.D0/DSQRT(1.D0 - VELR(I)*VELR(I))
|
| 2575 |
SCRCH2(I) = 1.D0 + UR(I) + PR(I)/RHOR(I)
|
| 2576 |
RR(I) = RHOR(I)*SCRCH1(I)
|
| 2577 |
MR(I) = RR(I)*SCRCH2(I)*SCRCH1(I)*VELR(I)
|
| 2578 |
ER(I) = RR(I)*SCRCH2(I)*SCRCH1(I) - PR(I) - RR(I)
|
| 2579 | |
| 2580 |
70 CONTINUE |
| 2581 | |
| 2582 |
RETURN
|
| 2583 |
END
|
| 2584 | |
| 2585 |
C -------- |
| 2586 |
CN NAME: A V R G 1 D |
| 2587 |
C -------- |
| 2588 | |
| 2589 |
CP PURPOSE: |
| 2590 |
CP THIS SUBROUTINE CALCULATES AVERAGES OF QUANTITIES P,RHO,VEL, OVER |
| 2591 |
CP THE PART OF THE DOMAIN OF DEPENDENCE FOR THE LAMBDA |
| 2592 |
CP CHARACTERISTIC OF RADM(I) FOR THE TIME INTERVAL (T(N),T(N+1)). |
| 2593 |
C |
| 2594 | |
| 2595 |
CC COMMENTS: |
| 2596 |
CC THIS ROUTINE CLOSELY FOLLOWS THE ANALYTICAL DEVELOPMENTS DESCRIBED IN |
| 2597 |
CC MARTI & MUELLER, JCP, 1996 |
| 2598 | |
| 2599 |
SUBROUTINE AVRG1D(N,DT,LAMB,PM,PP,DP,P6,RHOM,RHOP,DRHO,
|
| 2600 |
& RHO6,VELM,VELP,DVEL,VEL6,PL,PR,RHOL,RHOR, |
| 2601 |
& VELL,VELR) |
| 2602 | |
| 2603 |
IMPLICIT NONE
|
| 2604 | |
| 2605 |
INCLUDE 'size'
|
| 2606 | |
| 2607 |
C -------- |
| 2608 |
C ARGUMENTS |
| 2609 |
C -------- |
| 2610 | |
| 2611 |
INTEGER N
|
| 2612 | |
| 2613 |
DOUBLEPRECISION DT
|
| 2614 | |
| 2615 |
DOUBLEPRECISION LAMB(-4:MN5)
|
| 2616 | |
| 2617 |
DOUBLEPRECISION PM(-4:MN5),PP(-4:MN5),DP(-4:MN5),P6(-4:MN5),
|
| 2618 |
& RHOM(-4:MN5),RHOP(-4:MN5),DRHO(-4:MN5), |
| 2619 |
& RHO6(-4:MN5),VELM(-4:MN5),VELP(-4:MN5), |
| 2620 |
& DVEL(-4:MN5),VEL6(-4:MN5) |
| 2621 | |
| 2622 |
DOUBLEPRECISION PL(-4:MN6),PR(-4:MN6),RHOL(-4:MN6),RHOR(-4:MN6),
|
| 2623 |
& VELL(-4:MN6),VELR(-4:MN6) |
| 2624 | |
| 2625 |
C ------ |
| 2626 |
C COMMON BLOCKS |
| 2627 |
C ------ |
| 2628 | |
| 2629 |
DOUBLEPRECISION X(-4:MN5),XL(-4:MN5),XR(-4:MN5),DX(-4:MN5)
|
| 2630 |
COMMON /GRD/ X,XL,XR,DX
|
| 2631 | |
| 2632 |
C ---------- |
| 2633 |
C INTERNAL VARIABLES |
| 2634 |
C ---------- |
| 2635 | |
| 2636 |
INTEGER I
|
| 2637 | |
| 2638 |
DOUBLEPRECISION SCRCH1(-4:MN6)
|
| 2639 | |
| 2640 | |
| 2641 |
DO 10 I=0,N+1
|
| 2642 | |
| 2643 |
SCRCH1(I) = DMAX1(0.D0,DT*LAMB(I)/DX(I))
|
| 2644 | |
| 2645 |
10 CONTINUE |
| 2646 | |
| 2647 |
DO 20 I=1,N+1
|
| 2648 |
|
| 2649 |
PL(I) = PP(I-1) - SCRCH1(I-1)/2.D0*
|
| 2650 |
& (DP(I-1) - (1.D0 - 2.D0*SCRCH1(I-1)/3.D0)*P6(I-1)) |
| 2651 | |
| 2652 |
RHOL(I) = RHOP(I-1) - SCRCH1(I-1)/2.D0*
|
| 2653 |
& (DRHO(I-1) - (1.D0 - 2.D0*SCRCH1(I-1)/3.D0)*RHO6(I-1)) |
| 2654 | |
| 2655 |
VELL(I) = VELP(I-1) - SCRCH1(I-1)/2.D0*
|
| 2656 |
& (DVEL(I-1) - (1.D0 - 2.D0*SCRCH1(I-1)/3.D0)*VEL6(I-1)) |
| 2657 | |
| 2658 |
20 CONTINUE |
| 2659 | |
| 2660 |
DO 30 I=0,N+1
|
| 2661 | |
| 2662 |
SCRCH1(I) = DMAX1(0.D0,-DT*LAMB(I)/DX(I))
|
| 2663 | |
| 2664 |
30 CONTINUE |
| 2665 | |
| 2666 |
DO 40 I=1,N+1
|
| 2667 |
|
| 2668 |
PR(I) = PM(I) + SCRCH1(I)/2.D0*
|
| 2669 |
& (DP(I) + (1.D0 - 2.D0*SCRCH1(I)/3.D0)*P6(I)) |
| 2670 | |
| 2671 |
RHOR(I) = RHOM(I) + SCRCH1(I)/2.D0*
|
| 2672 |
& (DRHO(I) + (1.D0 - 2.D0*SCRCH1(I)/3.D0)*RHO6(I)) |
| 2673 | |
| 2674 |
VELR(I) = VELM(I) + SCRCH1(I)/2.D0*
|
| 2675 |
& (DVEL(I) + (1.D0 - 2.D0*SCRCH1(I)/3.D0)*VEL6(I)) |
| 2676 | |
| 2677 |
40 CONTINUE |
| 2678 | |
| 2679 |
RETURN
|
| 2680 |
END
|
| 2681 | |
| 2682 |
C -------- |
| 2683 |
CN NAME: N F L U X |
| 2684 |
C -------- |
| 2685 | |
| 2686 |
CP PURPOSE: |
| 2687 |
CP COMPUTES THE NUMERICAL FLUXES |
| 2688 |
C |
| 2689 | |
| 2690 |
CC COMMENTS: |
| 2691 |
CC COMPUTES THE NUMERICAL FLUXES FROM THE EXACT SOLUTION OF THE |
| 2692 |
CC RELATIVISTIC RIEMANN PROBLEM AS DESCRIBED IN MARTI AND MUELLER, JFM, |
| 2693 |
CC 1994 |
| 2694 |
|
| 2695 |
SUBROUTINE NFLUX(RHOL1,RHOR1,PL1,PR1,VELL1,VELR1,UL1,UR1,
|
| 2696 |
& CSL1,CSR1,FR,FM,FE) |
| 2697 | |
| 2698 |
IMPLICIT NONE
|
| 2699 | |
| 2700 |
C ----------- |
| 2701 |
C ARGUMENTS |
| 2702 |
C ----------- |
| 2703 | |
| 2704 |
DOUBLE PRECISION RHOL1, PL1, UL1, CSL1, VELL1,
|
| 2705 |
& RHOR1, PR1, UR1, CSR1, VELR1 |
| 2706 | |
| 2707 |
DOUBLE PRECISION FR, FM, FE
|
| 2708 | |
| 2709 |
C ------- |
| 2710 |
C COMMON BLOCKS |
| 2711 |
C ------- |
| 2712 | |
| 2713 |
DOUBLE PRECISION RHOL, PL, UL, HL, CSL, VELL, WL,
|
| 2714 |
& RHOR, PR, UR, HR, CSR, VELR, WR |
| 2715 |
COMMON /STATES/ RHOL, PL, UL, HL, CSL, VELL, WL,
|
| 2716 |
& RHOR, PR, UR, HR, CSR, VELR, WR |
| 2717 | |
| 2718 |
DOUBLE PRECISION RHOLS, ULS, HLS, CSLS, VELLS, VSHOCKL
|
| 2719 |
COMMON /LS/ RHOLS, ULS, HLS, CSLS, VELLS, VSHOCKL
|
| 2720 | |
| 2721 |
DOUBLE PRECISION RHORS, URS, HRS, CSRS, VELRS, VSHOCKR
|
| 2722 |
COMMON /RS/ RHORS, URS, HRS, CSRS, VELRS, VSHOCKR
|
| 2723 | |
| 2724 |
DOUBLE PRECISION GAMMA
|
| 2725 |
COMMON /ADIND/ GAMMA
|
| 2726 | |
| 2727 |
C --------- |
| 2728 |
C INTERNAL VARIABLES |
| 2729 |
C --------- |
| 2730 | |
| 2731 |
INTEGER ILOOP
|
| 2732 | |
| 2733 |
DOUBLE PRECISION TOL, PMIN, PMAX, DVEL1, DVEL2, CHECK
|
| 2734 | |
| 2735 |
DOUBLE PRECISION PS, VELS
|
| 2736 | |
| 2737 |
DOUBLE PRECISION RHOA, PA, VELA, UA
|
| 2738 | |
| 2739 |
DOUBLE PRECISION XI, XI1, XI2, XI3, XI4, XI5
|
| 2740 | |
| 2741 |
C ------------------------------ |
| 2742 |
C SPECIFIC ENTHALPY AND |
| 2743 |
C FLOW LORENTZ FACTORS IN THE INITIAL STATES |
| 2744 |
C ------------------------------ |
| 2745 | |
| 2746 |
RHOL = RHOL1
|
| 2747 |
RHOR = RHOR1
|
| 2748 | |
| 2749 |
PL = PL1
|
| 2750 |
PR = PR1
|
| 2751 | |
| 2752 |
UL = UL1
|
| 2753 |
UR = UR1
|
| 2754 | |
| 2755 |
VELL = VELL1
|
| 2756 |
VELR = VELR1
|
| 2757 | |
| 2758 |
CSL = CSL1
|
| 2759 |
CSR = CSR1
|
| 2760 | |
| 2761 |
HL = 1.D0+UL+PL/RHOL
|
| 2762 |
HR = 1.D0+UR+PR/RHOR
|
| 2763 | |
| 2764 |
WL = 1.D0/DSQRT(1.D0-VELL**2)
|
| 2765 |
WR = 1.D0/DSQRT(1.D0-VELR**2)
|
| 2766 | |
| 2767 |
C ------------- |
| 2768 |
C TOLERANCE FOR THE SOLUTION |
| 2769 |
C ------------- |
| 2770 | |
| 2771 |
TOL = 1.D-8
|
| 2772 | |
| 2773 |
C |
| 2774 | |
| 2775 |
ILOOP = 0
|
| 2776 | |
| 2777 |
PMIN = (PL + PR)/2.D0
|
| 2778 |
PMAX = PMIN
|
| 2779 | |
| 2780 |
5 ILOOP = ILOOP + 1 |
| 2781 | |
| 2782 |
PMIN = 0.5D0*MAX(PMIN,0.D0)
|
| 2783 |
PMAX = 2.D0*PMAX
|
| 2784 | |
| 2785 |
CALL GETDVEL(PMIN, DVEL1)
|
| 2786 | |
| 2787 |
CALL GETDVEL(PMAX, DVEL2)
|
| 2788 | |
| 2789 |
CHECK = DVEL1*DVEL2
|
| 2790 |
IF (CHECK.GT.0.D0) GOTO 5
|
| 2791 | |
| 2792 |
C --------------------------- |
| 2793 |
C PRESSURE AND FLOW VELOCITY IN THE INTERMEDIATE STATES |
| 2794 |
C --------------------------- |
| 2795 | |
| 2796 |
CALL GETP(PMIN, PMAX, TOL, PS)
|
| 2797 | |
| 2798 |
VELS = 0.5D0*(VELLS + VELRS)
|
| 2799 | |
| 2800 |
C --------------- |
| 2801 |
C SOLUTION ON THE NUMERICAL INTERFACE |
| 2802 |
C --------------- |
| 2803 | |
| 2804 |
C ----------- |
| 2805 |
C POSITIONS OF THE WAVES |
| 2806 |
C ----------- |
| 2807 | |
| 2808 |
IF (PL.GE.PS) THEN
|
| 2809 | |
| 2810 |
XI1 = (VELL - CSL)/(1.D0 - VELL*CSL)
|
| 2811 |
XI2 = (VELS - CSLS)/(1.D0 - VELS*CSLS)
|
| 2812 | |
| 2813 |
ELSE
|
| 2814 | |
| 2815 |
XI1 = VSHOCKL
|
| 2816 |
XI2 = XI1
|
| 2817 | |
| 2818 |
END IF
|
| 2819 | |
| 2820 |
XI3 = VELS
|
| 2821 | |
| 2822 |
IF (PR.GE.PS) THEN
|
| 2823 | |
| 2824 |
XI4 = (VELS + CSRS)/(1.D0 + VELS*CSRS)
|
| 2825 |
XI5 = (VELR + CSR)/(1.D0 + VELR*CSR)
|
| 2826 | |
| 2827 |
ELSE
|
| 2828 | |
| 2829 |
XI4 = VSHOCKR
|
| 2830 |
XI5 = XI4
|
| 2831 | |
| 2832 |
END IF
|
| 2833 | |
| 2834 |
C ---------- |
| 2835 |
C SOLUTION ON THE INTERFACE AT X = 0 (XI = 0) |
| 2836 |
C ---------- |
| 2837 | |
| 2838 |
XI = 0.D0
|
| 2839 | |
| 2840 |
IF (XI1.GE.XI) THEN
|
| 2841 | |
| 2842 |
PA = PL
|
| 2843 |
RHOA = RHOL
|
| 2844 |
VELA = VELL
|
| 2845 |
UA = UL
|
| 2846 | |
| 2847 |
ELSE IF (XI2.GE.XI) THEN
|
| 2848 | |
| 2849 |
CALL RAREF(XI,RHOL,CSL,VELL,'L',RHOA,PA,UA,VELA)
|
| 2850 | |
| 2851 |
ELSE IF (XI3.GE.XI) THEN
|
| 2852 | |
| 2853 |
PA = PS
|
| 2854 |
RHOA = RHOLS
|
| 2855 |
VELA = VELS
|
| 2856 |
UA = ULS
|
| 2857 | |
| 2858 |
ELSE IF (XI4.GE.XI) THEN
|
| 2859 | |
| 2860 |
PA = PS
|
| 2861 |
RHOA = RHORS
|
| 2862 |
VELA = VELS
|
| 2863 |
UA = URS
|
| 2864 | |
| 2865 |
ELSE IF (XI5.GE.XI) THEN
|
| 2866 | |
| 2867 |
CALL RAREF(XI,RHOR,CSR,VELR,'R',RHOA,PA,UA,VELA)
|
| 2868 | |
| 2869 |
ELSE
|
| 2870 | |
| 2871 |
PA = PR
|
| 2872 |
RHOA = RHOR
|
| 2873 |
VELA = VELR
|
| 2874 |
UA = UR
|
| 2875 | |
| 2876 |
END IF
|
| 2877 | |
| 2878 |
C ----------- |
| 2879 |
C NUMERICAL FLUXES |
| 2880 |
C ----------- |
| 2881 | |
| 2882 |
FR = RHOA*VELA/DSQRT(1.D0 - VELA**2)
|
| 2883 |
FM = RHOA*(1.D0 + UA + PA/RHOA)*VELA**2/(1.D0 - VELA**2) + PA
|
| 2884 |
FE = RHOA*(1.D0 + UA + PA/RHOA)*VELA/(1.D0 - VELA**2) -
|
| 2885 |
& RHOA*VELA/DSQRT(1.D0 - VELA**2) |
| 2886 |
|
| 2887 |
RETURN
|
| 2888 |
END
|
| 2889 | |
| 2890 |
C ---------- |
| 2891 |
CN NAME: G E T D V E L |
| 2892 |
C ---------- |
| 2893 | |
| 2894 |
CP PURPOSE: |
| 2895 |
CP COMPUTE THE DIFFERENCE IN FLOW SPEED BETWEEN LEFT AND RIGHT INTERMEDIATE |
| 2896 |
CP STATES FOR GIVEN LEFT AND RIGHT STATES AND PRESSURE |
| 2897 |
C |
| 2898 | |
| 2899 |
CC COMMENTS: |
| 2900 |
CC NONE |
| 2901 |
C |
| 2902 |
SUBROUTINE GETDVEL( P, DVEL)
|
| 2903 | |
| 2904 |
IMPLICIT NONE
|
| 2905 | |
| 2906 |
C ----- |
| 2907 |
C ARGUMENTS |
| 2908 |
C ----- |
| 2909 | |
| 2910 |
DOUBLEPRECISION P, DVEL
|
| 2911 | |
| 2912 |
C ------- |
| 2913 |
C COMMON BLOCKS |
| 2914 |
C ------- |
| 2915 | |
| 2916 |
DOUBLE PRECISION RHOLS,ULS,HLS,CSLS,VELLS,VSHOCKL
|
| 2917 |
COMMON /LS/ RHOLS,ULS,HLS,CSLS,VELLS,VSHOCKL
|
| 2918 | |
| 2919 |
DOUBLE PRECISION RHORS,URS,HRS,CSRS,VELRS,VSHOCKR
|
| 2920 |
COMMON /RS/ RHORS,URS,HRS,CSRS,VELRS,VSHOCKR
|
| 2921 | |
| 2922 |
DOUBLE PRECISION RHOL, PL, UL, HL, CSL, VELL, WL,
|
| 2923 |
& RHOR, PR, UR, HR, CSR, VELR, WR |
| 2924 |
COMMON /STATES/ RHOL, PL, UL, HL, CSL, VELL, WL,
|
| 2925 |
& RHOR, PR, UR, HR, CSR, VELR, WR |
| 2926 | |
| 2927 |
DOUBLE PRECISION GAMMA
|
| 2928 |
COMMON /ADIND/ GAMMA
|
| 2929 | |
| 2930 |
C ----- |
| 2931 |
C LEFT WAVE |
| 2932 |
C ----- |
| 2933 | |
| 2934 |
CALL GETVEL(P, RHOL, PL, UL, HL, CSL, VELL, WL, 'L',
|
| 2935 |
& RHOLS, ULS, HLS, CSLS, VELLS, VSHOCKL) |
| 2936 | |
| 2937 |
C ----- |
| 2938 |
C RIGHT WAVE |
| 2939 |
C ----- |
| 2940 | |
| 2941 |
CALL GETVEL(P, RHOR, PR, UR, HR, CSR, VELR, WR, 'R',
|
| 2942 |
& RHORS, URS, HRS, CSRS, VELRS, VSHOCKR) |
| 2943 | |
| 2944 |
DVEL = VELLS - VELRS
|
| 2945 | |
| 2946 |
RETURN
|
| 2947 |
END
|
| 2948 | |
| 2949 |
C ------- |
| 2950 |
CN NAME: G E T P |
| 2951 |
C ------- |
| 2952 | |
| 2953 |
CP PURPOSE: |
| 2954 |
CP FIND THE PRESSURE IN THE INTERMEDIATE STATE OF A RIEMANN PROBLEM IN |
| 2955 |
CP RELATIVISTIC HYDRODYNAMICS |
| 2956 |
C |
| 2957 | |
| 2958 |
CC COMMENTS: |
| 2959 |
CC THIS ROUTINE USES A COMBINATION OF INTERVAL BISECTION AND INVERSE |
| 2960 |
CC QUADRATIC INTERPOLATION TO FIND THE ROOT IN A SPECIFIED INTERVAL. |
| 2961 |
CC IT IS ASSUMED THAT DVEL(PMIN) AND DVEL(PMAX) HAVE OPPOSITE SIGNS WITHOUT |
| 2962 |
CC A CHECK. |
| 2963 |
CC ADAPTED FROM "COMPUTER METHODS FOR MATHEMATICAL COMPUTATION", |
| 2964 |
CC BY G. E. FORSYTHE, M. A. MALCOLM, AND C. B. MOLER, |
| 2965 |
CC PRENTICE-HALL, ENGLEWOOD CLIFFS N.J. |
| 2966 |
C |
| 2967 |
SUBROUTINE GETP( PMIN, PMAX, TOL, PS)
|
| 2968 | |
| 2969 |
IMPLICIT NONE
|
| 2970 | |
| 2971 |
C ----- |
| 2972 |
C ARGUMENTS |
| 2973 |
C ----- |
| 2974 | |
| 2975 |
DOUBLEPRECISION PMIN, PMAX, TOL, PS
|
| 2976 | |
| 2977 |
C ------- |
| 2978 |
C COMMON BLOCKS |
| 2979 |
C ------- |
| 2980 | |
| 2981 |
DOUBLEPRECISION GAMMA
|
| 2982 |
COMMON /ADIND/ GAMMA
|
| 2983 | |
| 2984 |
DOUBLEPRECISION RHOL, PL, UL, HL, CSL, VELL, WL,
|
| 2985 |
& RHOR, PR, UR, HR, CSR, VELR, WR |
| 2986 |
COMMON /STATES/ RHOL, PL, UL, HL, CSL, VELL, WL,
|
| 2987 |
& RHOR, PR, UR, HR, CSR, VELR, WR |
| 2988 | |
| 2989 |
C --------- |
| 2990 |
C INTERNAL VARIABLES |
| 2991 |
C --------- |
| 2992 | |
| 2993 |
DOUBLEPRECISION A, B, C, D, E, EPS, FA, FB, FC, TOL1,
|
| 2994 |
& XM, P, Q, R, S |
| 2995 | |
| 2996 |
C ------------- |
| 2997 |
C COMPUTE MACHINE PRECISION |
| 2998 |
C ------------- |
| 2999 | |
| 3000 |
EPS = 1.D0
|
| 3001 |
10 EPS = EPS/2.D0 |
| 3002 |
TOL1 = 1.D0 + EPS
|
| 3003 |
IF( TOL1 .GT. 1.D0) GO TO 10
|
| 3004 | |
| 3005 |
C ------- |
| 3006 |
C INITIALIZATION |
| 3007 |
C ------- |
| 3008 | |
| 3009 |
A = PMIN
|
| 3010 |
B = PMAX
|
| 3011 |
CALL GETDVEL(A,FA)
|
| 3012 |
CALL GETDVEL(B,FB)
|
| 3013 | |
| 3014 |
C ----- |
| 3015 |
C BEGIN STEP |
| 3016 |
C ----- |
| 3017 | |
| 3018 |
20 C = A |
| 3019 |
FC = FA
|
| 3020 |
D = B - A
|
| 3021 |
E = D
|
| 3022 |
30 IF( DABS(FC) .GE. DABS(FB))GO TO 40 |
| 3023 |
A = B
|
| 3024 |
B = C
|
| 3025 |
C = A
|
| 3026 |
FA = FB
|
| 3027 |
FB = FC
|
| 3028 |
FC = FA
|
| 3029 | |
| 3030 |
C -------- |
| 3031 |
C CONVERGENCE TEST |
| 3032 |
C -------- |
| 3033 | |
| 3034 |
40 TOL1 = 2.D0*EPS*DABS(B) + 0.5D0*TOL |
| 3035 |
XM = 0.5D0*(C - B)
|
| 3036 |
IF( DABS(XM) .LE. TOL1) GO TO 90
|
| 3037 |
IF( FB .EQ. 0.D0) GO TO 90
|
| 3038 | |
| 3039 |
C ------------ |
| 3040 |
C IS BISECTION NECESSARY? |
| 3041 |
C ------------ |
| 3042 | |
| 3043 |
IF( DABS(E) .LT. TOL1) GO TO 70
|
| 3044 |
IF( DABS(FA) .LE. DABS(FB)) GO TO 70
|
| 3045 | |
| 3046 |
C ------------------ |
| 3047 |
C IS QUADRATIC INTERPOLATION POSSIBLE? |
| 3048 |
C ------------------ |
| 3049 | |
| 3050 |
IF( A .NE. C) GO TO 50
|
| 3051 | |
| 3052 |
C ---------- |
| 3053 |
C LINEAR INTERPOLATION |
| 3054 |
C ---------- |
| 3055 | |
| 3056 |
S = FB/FA
|
| 3057 |
P = 2.D0*XM*S
|
| 3058 |
Q = 1.D0 - S
|
| 3059 |
GO TO 60
|
| 3060 | |
| 3061 |
C ---------------- |
| 3062 |
C INVERSE QUADRATIC INTERPOLATION |
| 3063 |
C ---------------- |
| 3064 | |
| 3065 |
50 Q = FA/FC |
| 3066 |
R = FB/FC
|
| 3067 |
S = FB/FA
|
| 3068 |
P = S*(2.D0*XM*Q*(Q - R) - (B - A)*(R - 1.D0))
|
| 3069 |
Q = (Q - 1.D0)*(R - 1.D0)*(S - 1.D0)
|
| 3070 | |
| 3071 |
C ------ |
| 3072 |
C ADJUST SIGNS |
| 3073 |
C ------ |
| 3074 | |
| 3075 |
60 IF( P .GT. 0.D0) Q = -Q |
| 3076 |
P = DABS(P)
|
| 3077 | |
| 3078 |
C -------------- |
| 3079 |
C IS INTERPOLATION ACCEPTABLE? |
| 3080 |
C -------------- |
| 3081 | |
| 3082 |
IF( (2.D0*P) .GE. (3.D0*XM*Q-DABS(TOL1*Q))) GO TO 70
|
| 3083 |
IF( P .GE. DABS(0.5D0*E*Q)) GO TO 70
|
| 3084 |
E = D
|
| 3085 |
D = P/Q
|
| 3086 |
GO TO 80
|
| 3087 | |
| 3088 |
C ----- |
| 3089 |
C BISECTION |
| 3090 |
C ----- |
| 3091 | |
| 3092 |
70 D = XM |
| 3093 |
E = D
|
| 3094 | |
| 3095 |
C ------- |
| 3096 |
C COMPLETE STEP |
| 3097 |
C ------- |
| 3098 | |
| 3099 |
80 A = B |
| 3100 |
FA = FB
|
| 3101 |
IF( DABS(D) .GT. TOL1) B = B+D
|
| 3102 |
IF( DABS(D) .LE. TOL1) B = B+DSIGN(TOL1,XM)
|
| 3103 |
CALL GETDVEL(B,FB)
|
| 3104 |
IF( (FB*(FC/DABS(FC))) .GT. 0.D0) GO TO 20
|
| 3105 |
GO TO 30
|
| 3106 | |
| 3107 |
C -- |
| 3108 |
C DONE |
| 3109 |
C -- |
| 3110 | |
| 3111 |
90 PS = B |
| 3112 | |
| 3113 |
RETURN
|
| 3114 |
END
|
| 3115 | |
| 3116 |
C --------- |
| 3117 |
CN NAME: G E T V E L |
| 3118 |
C --------- |
| 3119 | |
| 3120 |
CP PURPOSE: |
| 3121 |
CP COMPUTE THE FLOW VELOCITY BEHIND A RAREFACTION OR SHOCK IN TERMS OF THE |
| 3122 |
CP POST-WAVE PRESSURE FOR A GIVEN STATE AHEAD THE WAVE IN A RELATIVISTIC |
| 3123 |
CP FLOW |
| 3124 |
C |
| 3125 | |
| 3126 |
CC COMMENTS: |
| 3127 |
CC THIS ROUTINE CLOSELY FOLLOWS THE EXPRESSIONS IN MARTI AND MUELLER, |
| 3128 |
CC J. FLUID MECH., (1994) |
| 3129 | |
| 3130 |
SUBROUTINE GETVEL( P, RHOA, PA, UA, HA, CSA, VELA, WA, S,
|
| 3131 |
& RHO, U, H, CS, VEL, VSHOCK) |
| 3132 | |
| 3133 |
IMPLICIT NONE
|
| 3134 | |
| 3135 |
C ----- |
| 3136 |
C ARGUMENTS |
| 3137 |
C ----- |
| 3138 | |
| 3139 |
DOUBLE PRECISION P, RHOA, PA, UA, HA, CSA, VELA, WA
|
| 3140 |
CHARACTER*1 S
|
| 3141 |
DOUBLE PRECISION RHO, U, H, CS, VEL, VSHOCK
|
| 3142 | |
| 3143 |
C ------- |
| 3144 |
C COMMON BLOCKS |
| 3145 |
C ------- |
| 3146 | |
| 3147 |
DOUBLE PRECISION GAMMA
|
| 3148 |
COMMON /ADIND/ GAMMA
|
| 3149 | |
| 3150 |
C --------- |
| 3151 |
C INTERNAL VARIABLES |
| 3152 |
C --------- |
| 3153 | |
| 3154 |
DOUBLE PRECISION A, B, C, SIGN
|
| 3155 |
DOUBLE PRECISION J, WSHOCK
|
| 3156 |
DOUBLE PRECISION K, SQGL1
|
| 3157 | |
| 3158 |
C --------------- |
| 3159 |
C LEFT OR RIGHT PROPAGATING WAVE |
| 3160 |
C --------------- |
| 3161 | |
| 3162 |
IF (S.EQ.'L') SIGN = -1.D0
|
| 3163 | |
| 3164 |
IF (S.EQ.'R') SIGN = 1.D0
|
| 3165 | |
| 3166 |
C |
| 3167 | |
| 3168 |
IF (P/PA - 1.D0.GT.1.D-10) THEN
|
| 3169 | |
| 3170 |
C --- |
| 3171 |
C SHOCK |
| 3172 |
C --- |
| 3173 | |
| 3174 |
A = 1.D0+(GAMMA-1.D0)*(PA-P)/GAMMA/P
|
| 3175 |
B = 1.D0-A
|
| 3176 |
C = HA*(PA-P)/RHOA-HA**2
|
| 3177 | |
| 3178 |
C ---------------- |
| 3179 |
C CHECK FOR UNPHYSICAL ENTHALPIES |
| 3180 |
C ---------------- |
| 3181 | |
| 3182 |
IF (C.GT.(B**2/4.D0/A)) STOP
|
| 3183 |
& 'GETVEL: UNPHYSICAL SPECIFIC ENTHALPY IN INTERMEDIATE STATE' |
| 3184 | |
| 3185 |
C ----------------------------- |
| 3186 |
C SPECIFIC ENTHALPY IN THE POST-WAVE STATE |
| 3187 |
C (FROM THE EQUATION OF STATE AND THE TAUB ADIABAT, |
| 3188 |
C EQ.(74), MM94) |
| 3189 |
C ----------------------------- |
| 3190 | |
| 3191 |
H = (-B+DSQRT(B**2-4.D0*A*C))/2.D0/A
|
| 3192 | |
| 3193 |
C --------------- |
| 3194 |
C DENSITY IN THE POST-WAVE STATE |
| 3195 |
C (FROM EQ.(73), MM94) |
| 3196 |
C --------------- |
| 3197 | |
| 3198 |
RHO = GAMMA*P/(GAMMA-1.D0)/(H-1.D0)
|
| 3199 | |
| 3200 |
C ------------------------ |
| 3201 |
C SPECIFIC INTERNAL ENERGY IN THE POST-WAVE STATE |
| 3202 |
C (FROM THE EQUATION OF STATE) |
| 3203 |
C ------------------------ |
| 3204 | |
| 3205 |
U = P/(GAMMA-1.D0)/RHO
|
| 3206 | |
| 3207 |
C -------------------------- |
| 3208 |
C MASS FLUX ACROSS THE WAVE |
| 3209 |
C (FROM THE RANKINE-HUGONIOT RELATIONS, EQ.(71), MM94) |
| 3210 |
C -------------------------- |
| 3211 | |
| 3212 |
J = SIGN*DSQRT((P-PA)/(HA/RHOA-H/RHO))
|
| 3213 | |
| 3214 |
C ---------- |
| 3215 |
C SHOCK VELOCITY |
| 3216 |
C (FROM EQ.(86), MM94 |
| 3217 |
C ---------- |
| 3218 | |
| 3219 |
A = J**2+(RHOA*WA)**2
|
| 3220 |
B = -VELA*RHOA**2*WA**2
|
| 3221 |
VSHOCK = (-B+SIGN*J**2*DSQRT(1.D0+RHOA**2/J**2))/A
|
| 3222 |
WSHOCK = 1.D0/DSQRT(1.D0-VSHOCK**2)
|
| 3223 | |
| 3224 |
C ------------------- |
| 3225 |
C FLOW VELOCITY IN THE POST-SHOCK STATE |
| 3226 |
C (FROM EQ.(67), MM94) |
| 3227 |
C ------------------- |
| 3228 | |
| 3229 |
A = WSHOCK*(P-PA)/J+HA*WA*VELA
|
| 3230 |
B = HA*WA+(P-PA)*(WSHOCK*VELA/J+1.D0/RHOA/WA)
|
| 3231 | |
| 3232 |
VEL = A/B
|
| 3233 | |
| 3234 |
C --------------------- |
| 3235 |
C LOCAL SOUND SPEED IN THE POST-SHOCK STATE |
| 3236 |
C (FROM THE EQUATION OF STATE) |
| 3237 |
C --------------------- |
| 3238 | |
| 3239 |
CS = DSQRT(GAMMA*P/RHO/H)
|
| 3240 | |
| 3241 |
ELSE IF (P/PA - 1.D0.GT.0.D0) THEN
|
| 3242 |
|
| 3243 |
C -------------- |
| 3244 |
C ALMOST CONSTANT INTERMEDIATE STATE |
| 3245 |
C -------------- |
| 3246 | |
| 3247 |
RHO = RHOA
|
| 3248 |
U = UA
|
| 3249 |
H = 1.D0 + U + P/RHO
|
| 3250 |
CS = DSQRT(GAMMA*P/RHO/H)
|
| 3251 |
VEL = VELA
|
| 3252 |
VSHOCK = VELA
|
| 3253 | |
| 3254 |
ELSE
|
| 3255 | |
| 3256 |
C ------ |
| 3257 |
C RAREFACTION |
| 3258 |
C ------ |
| 3259 | |
| 3260 |
C --------------------------- |
| 3261 |
C POLITROPIC CONSTANT OF THE GAS ACROSS THE RAREFACTION |
| 3262 |
C --------------------------- |
| 3263 | |
| 3264 |
K = PA/RHOA**GAMMA
|
| 3265 | |
| 3266 |
C --------------- |
| 3267 |
C DENSITY BEHIND THE RAREFACTION |
| 3268 |
C --------------- |
| 3269 | |
| 3270 |
RHO = (P/K)**(1.D0/GAMMA)
|
| 3271 | |
| 3272 |
C ------------------------ |
| 3273 |
C SPECIFIC INTERNAL ENERGY BEHIND THE RAREFACTION |
| 3274 |
C (FROM THE EQUATION OF STATE) |
| 3275 |
C ------------------------ |
| 3276 | |
| 3277 |
U = P/(GAMMA-1.D0)/RHO
|
| 3278 | |
| 3279 |
C ----------- |
| 3280 |
C SPECIFIC ENTHALPY |
| 3281 |
C ----------- |
| 3282 | |
| 3283 |
H = 1.D0 + U + P/RHO
|
| 3284 |
C -------------------- |
| 3285 |
C LOCAL SOUND SPEED BEHIND THE RAREFACTION |
| 3286 |
C (FROM THE EQUATION OF STATE) |
| 3287 |
C -------------------- |
| 3288 | |
| 3289 |
CS = DSQRT(GAMMA*P/RHO/H)
|
| 3290 | |
| 3291 |
C ------------------ |
| 3292 |
C FLOW VELOCITY BEHIND THE RAREFACTION |
| 3293 |
C ------------------ |
| 3294 | |
| 3295 |
SQGL1 = DSQRT(GAMMA-1.D0)
|
| 3296 |
A = (1.D0+VELA)/(1.D0-VELA)*
|
| 3297 |
& ((SQGL1+CSA)/(SQGL1-CSA)* |
| 3298 |
& (SQGL1-CS)/(SQGL1+CS))**(-SIGN*2.D0/SQGL1) |
| 3299 | |
| 3300 |
VEL = (A-1.D0)/(A+1.D0)
|
| 3301 | |
| 3302 |
END IF
|
| 3303 |
END
|
| 3304 | |
| 3305 |
C -------- |
| 3306 |
CN NAME: R A R E F |
| 3307 |
C -------- |
| 3308 | |
| 3309 |
CP PURPOSE: |
| 3310 |
CP COMPUTE THE FLOW STATE IN A RAREFACTION FOR GIVEN PRE-WAVE STATE |
| 3311 |
C |
| 3312 | |
| 3313 |
CC COMMENTS: |
| 3314 |
CC THIS ROUTINE CLOSELY FOLLOWS THE EXPRESSIONS IN MARTI AND MUELLER, |
| 3315 |
CC J. FLUID MECH., (1994) |
| 3316 | |
| 3317 |
SUBROUTINE RAREF( XI, RHOA, CSA, VELA, S, RHO, P, U, VEL)
|
| 3318 | |
| 3319 |
IMPLICIT NONE
|
| 3320 | |
| 3321 |
C ----- |
| 3322 |
C ARGUMENTS |
| 3323 |
C ----- |
| 3324 | |
| 3325 |
DOUBLE PRECISION XI
|
| 3326 | |
| 3327 |
DOUBLE PRECISION RHOA, CSA, VELA
|
| 3328 | |
| 3329 |
CHARACTER S
|
| 3330 | |
| 3331 |
DOUBLE PRECISION RHO, P, U, VEL
|
| 3332 | |
| 3333 |
C ------- |
| 3334 |
C COMMON BLOCKS |
| 3335 |
C ------- |
| 3336 | |
| 3337 |
DOUBLE PRECISION GAMMA
|
| 3338 |
COMMON /ADIND/ GAMMA
|
| 3339 | |
| 3340 |
C --------- |
| 3341 |
C INTERNAL VARIABLES |
| 3342 |
C --------- |
| 3343 | |
| 3344 |
DOUBLE PRECISION B, C, D, K, L, V, OCS2, FCS2, DFDCS2, CS2, SIGN
|
| 3345 | |
| 3346 |
C --------------- |
| 3347 |
C LEFT OR RIGHT PROPAGATING WAVE |
| 3348 |
C --------------- |
| 3349 | |
| 3350 |
IF (S.EQ.'L') SIGN = 1.D0
|
| 3351 | |
| 3352 |
IF (S.EQ.'R') SIGN = -1.D0
|
| 3353 | |
| 3354 |
B = DSQRT(GAMMA - 1.D0)
|
| 3355 |
C = (B + CSA)/(B - CSA)
|
| 3356 |
D = -SIGN*B/2.D0
|
| 3357 |
K = (1.D0 + XI)/(1.D0 - XI)
|
| 3358 |
L = C*K**D
|
| 3359 |
V = ((1.D0 - VELA)/(1.D0 + VELA))**D
|
| 3360 | |
| 3361 |
OCS2 = CSA
|
| 3362 | |
| 3363 |
25 FCS2 = L*V*(1.D0 + SIGN*OCS2)**D*(OCS2 - B) + |
| 3364 |
& (1.D0 - SIGN*OCS2)**D*(OCS2 + B) |
| 3365 | |
| 3366 |
DFDCS2 = L*V*(1.D0 + SIGN*OCS2)**D*
|
| 3367 |
& (1.D0 + SIGN*D*(OCS2 - B)/(1.D0 + SIGN*OCS2)) + |
| 3368 |
& (1.D0 - SIGN*OCS2)**D* |
| 3369 |
& (1.D0 - SIGN*D*(OCS2 + B)/(1.D0 - SIGN*OCS2)) |
| 3370 | |
| 3371 |
CS2 = OCS2 - FCS2/DFDCS2
|
| 3372 | |
| 3373 |
IF (ABS(CS2 - OCS2)/OCS2.GT.5.E-7)THEN
|
| 3374 |
OCS2 = CS2
|
| 3375 |
GOTO 25
|
| 3376 |
END IF
|
| 3377 | |
| 3378 |
VEL = (XI + SIGN*CS2)/(1.D0 + SIGN*XI*CS2)
|
| 3379 | |
| 3380 |
RHO = RHOA*((CS2**2*(GAMMA - 1.D0 - CSA**2))/
|
| 3381 |
& (CSA**2*(GAMMA - 1.D0 - CS2**2))) |
| 3382 |
& **(1.D0/(GAMMA - 1.D0)) |
| 3383 | |
| 3384 |
P = CS2**2*(GAMMA - 1.D0)*RHO/(GAMMA - 1.D0 - CS2**2)/GAMMA
|
| 3385 | |
| 3386 |
U = P/(GAMMA - 1.D0)/RHO
|
| 3387 | |
| 3388 |
RETURN
|
| 3389 |
END
|
| 3390 | |
| 3391 |
C -------- |
| 3392 |
CN NAME: F I L N A M |
| 3393 |
C -------- |
| 3394 | |
| 3395 |
CP PURPOSE: |
| 3396 |
CP CONSTRUCTS NEW FILENAMES FOR OUTPUT AND RESTART FILES |
| 3397 |
C |
| 3398 | |
| 3399 |
CC COMMENTS: |
| 3400 |
CC NONE |
| 3401 | |
| 3402 |
SUBROUTINE FILNAM
|
| 3403 | |
| 3404 |
IMPLICIT NONE
|
| 3405 | |
| 3406 |
C --------- |
| 3407 |
C COMMON BLOCKS |
| 3408 |
C --------- |
| 3409 | |
| 3410 |
CHARACTER*7 OUTFIL
|
| 3411 |
CHARACTER*8 LABEL
|
| 3412 |
CHARACTER*4 BASENM
|
| 3413 |
CHARACTER*2 SUFFIX
|
| 3414 |
CHARACTER*1 SF1,SF2
|
| 3415 | |
| 3416 |
COMMON /CHRC/ LABEL,OUTFIL,BASENM,SUFFIX
|
| 3417 | |
| 3418 |
C --------- |
| 3419 |
C INTERNAL VARIABLES |
| 3420 |
C --------- |
| 3421 | |
| 3422 |
INTEGER ISF1,ISF2
|
| 3423 | |
| 3424 |
IF (SUFFIX(2:2).EQ.'z'.OR.SUFFIX(2:2).EQ.'Z') THEN
|
| 3425 |
SF1 = SUFFIX(1:1)
|
| 3426 |
ISF1 = ICHAR(SF1)
|
| 3427 |
SF2 = SUFFIX(2:2)
|
| 3428 |
ISF2 = ICHAR(SF2)
|
| 3429 | |
| 3430 |
ISF1 = ISF1 + 1
|
| 3431 |
ISF2 = ISF2 - 25
|
| 3432 |
SUFFIX(1:1) = CHAR(ISF1)
|
| 3433 |
SUFFIX(2:2) = CHAR(ISF2)
|
| 3434 |
ELSE
|
| 3435 |
SF2 = SUFFIX(2:2)
|
| 3436 |
ISF2 = ICHAR(SF2)
|
| 3437 |
ISF2 = ISF2 + 1
|
| 3438 |
SUFFIX(2:2) = CHAR(ISF2)
|
| 3439 |
END IF
|
| 3440 | |
| 3441 |
OUTFIL = BASENM // 'O' // SUFFIX
|
| 3442 | |
| 3443 |
RETURN
|
| 3444 |
END
|
| 3445 | |
| 3446 |
C -------- |
| 3447 |
CN NAME: G E T P R F Q |
| 3448 |
C -------- |
| 3449 | |
| 3450 |
CP PURPOSE: |
| 3451 |
CP COMPUTE THE PRIMITIVE QUANTITIES FROM THE CONSERVED ONES |
| 3452 |
C |
| 3453 | |
| 3454 |
CC COMMENTS: |
| 3455 |
CC PRIMITIVE VARIABLES ARE OBTAINED BY SOLVING AN IMPLICIT EQUATION FOR |
| 3456 |
CC THE PRESSURE BY MEANS OF A NEWTON-RAPHSON METHOD. HARDWIRED FOR A |
| 3457 |
CC CONSTANT-GAMMA IDEAL GAS |
| 3458 | |
| 3459 |
SUBROUTINE GETPRFQ(N,R,M,E,
|
| 3460 |
& VEL,W,RHO,U,P,H,CS,DPDRH,DPDU) |
| 3461 | |
| 3462 |
IMPLICIT NONE
|
| 3463 | |
| 3464 |
INCLUDE 'size'
|
| 3465 | |
| 3466 |
C ------- |
| 3467 |
C ARGUMENTS |
| 3468 |
C ------- |
| 3469 | |
| 3470 |
INTEGER N
|
| 3471 | |
| 3472 |
DOUBLEPRECISION P(-4:MN5),RHO(-4:MN5),VEL(-4:MN5),
|
| 3473 |
& U(-4:MN5),CS(-4:MN5),W(-4:MN5),H(-4:MN5), |
| 3474 |
& DPDRH(-4:MN5),DPDU(-4:MN5) |
| 3475 | |
| 3476 |
DOUBLEPRECISION R(-4:MN5),M(-4:MN5),E(-4:MN5)
|
| 3477 | |
| 3478 |
C --------- |
| 3479 |
C COMMON BLOCKS |
| 3480 |
C --------- |
| 3481 | |
| 3482 |
INTEGER NEND,NOUT,ITSTP,NX
|
| 3483 |
COMMON /INPTI/ NEND,NOUT,ITSTP,NX
|
| 3484 | |
| 3485 |
DOUBLEPRECISION TMAX,TOUT,CFL,DTINI,SMALL,SMLRHO,SMALLP,
|
| 3486 |
& SMALLU,GRIDLX,EPSILN,ETA1,ETA2,EPSLN,AK0,OMG1,OMG2 |
| 3487 |
COMMON /INPTF/ TMAX,TOUT,CFL,DTINI,SMALL,SMLRHO,SMALLP,
|
| 3488 |
& SMALLU,GRIDLX,EPSILN,ETA1,ETA2,EPSLN,AK0,OMG1,OMG2 |
| 3489 | |
| 3490 |
DOUBLEPRECISION GB
|
| 3491 |
COMMON /ADIND/ GB
|
| 3492 | |
| 3493 |
DOUBLEPRECISION TIME,DT
|
| 3494 |
COMMON /ZEIT/ TIME,DT
|
| 3495 | |
| 3496 |
C --------- |
| 3497 |
C INTERNAL VARIABLES |
| 3498 |
C --------- |
| 3499 | |
| 3500 |
INTEGER I,COUNT
|
| 3501 | |
| 3502 |
DOUBLEPRECISION MOMENT,VELCTY
|
| 3503 | |
| 3504 |
DOUBLEPRECISION PMIN(-4:MN5),PMAX,OP(-4:MN5)
|
| 3505 | |
| 3506 |
DOUBLEPRECISION FP,DFDP,ERRP
|
| 3507 | |
| 3508 |
DO 5 I=1,N
|
| 3509 | |
| 3510 |
R(I) = DMAX1(R(I),SMLRHO)
|
| 3511 |
E(I) = DMAX1(E(I),SMALLU)
|
| 3512 | |
| 3513 |
5 CONTINUE |
| 3514 | |
| 3515 |
DO 9 I=1,N
|
| 3516 | |
| 3517 |
COUNT = 0
|
| 3518 | |
| 3519 |
MOMENT = DABS(M(I))
|
| 3520 |
PMIN(I) = DMAX1(MOMENT - E(I) - R(I) + MOMENT*SMALL,SMALLP)
|
| 3521 |
PMAX = (GB-1.D0)*E(I)
|
| 3522 |
IF (PMIN(I).GT.PMAX) GOTO 990
|
| 3523 | |
| 3524 |
OP(I) = 0.5D0*(PMIN(I)+PMAX)
|
| 3525 | |
| 3526 |
8 COUNT = COUNT + 1 |
| 3527 |
OP(I) = DMAX1(OP(I),PMIN(I))
|
| 3528 |
VELCTY = MOMENT/(E(I) + R(I) + OP(I))
|
| 3529 |
W(I) = 1.D0/DSQRT(1.D0 - VELCTY*VELCTY)
|
| 3530 |
FP = (GB - 1.D0)*(E(I) + R(I)*(1.D0 - W(I))+
|
| 3531 |
& OP(I)*(1.D0 - W(I)*W(I)))/W(I)/W(I) - OP(I) |
| 3532 |
DFDP = (GB - 1.D0)*VELCTY*VELCTY*
|
| 3533 |
& (E(I) + R(I)*(1.D0 - W(I))+OP(I))/ |
| 3534 |
& (E(I) + R(I) + OP(I)) - 1.D0 |
| 3535 | |
| 3536 |
P(I) = DMAX1(OP(I) - FP/DFDP,PMIN(I))
|
| 3537 | |
| 3538 |
ERRP = DABS(1.D0 - P(I)/OP(I))
|
| 3539 | |
| 3540 |
OP(I) = P(I)
|
| 3541 | |
| 3542 |
IF (COUNT.GE.10000) GOTO 999
|
| 3543 | |
| 3544 |
IF (ERRP.GT.1.D-8) GOTO 8
|
| 3545 | |
| 3546 |
VEL(I) = M(I)/(E(I)+R(I)+OP(I))
|
| 3547 |
IF (DABS(VEL(I)) .LT.SMALL*SMALL) VEL(I) = 0.D0
|
| 3548 | |
| 3549 |
RHO(I) = R(I)/W(I)
|
| 3550 | |
| 3551 |
9 CONTINUE |
| 3552 | |
| 3553 |
DO 30 I=1,N
|
| 3554 | |
| 3555 |
U(I) = P(I)/(GB - 1.D0)/RHO(I)
|
| 3556 | |
| 3557 |
IF (P(I).EQ.PMIN(I)) THEN
|
| 3558 |
WRITE(6,*) 'GETPRFQ: MINIMUM PRESSURE REACHED AT POINT:'
|
| 3559 |
WRITE(6,*) ' I = ', I,' T = ', TIME
|
| 3560 |
END IF
|
| 3561 | |
| 3562 |
30 CONTINUE |
| 3563 | |
| 3564 |
CALL EOS(N,RHO,U,GB,P,H,CS,DPDRH,DPDU)
|
| 3565 | |
| 3566 |
GOTO 1000
|
| 3567 | |
| 3568 |
990 WRITE(6,*) 'GETPRFQ: NO PHYSICAL PRESSURE AVAILABLE' |
| 3569 |
WRITE(6,*) ' T = ', TIME
|
| 3570 |
WRITE(6,*) ' I = ', I
|
| 3571 |
WRITE(6,*) ' R = ', R(I), ' MOMENT = ', MOMENT
|
| 3572 |
WRITE(6,*) ' E = ', E(I)
|
| 3573 |
WRITE(6,*) ' MOMENT-E-D = ', MOMENT - R(I) - E(I)
|
| 3574 |
WRITE(6,*) ' (GB-1)E = ', (GB - 1.D0)*E(I)
|
| 3575 |
STOP
|
| 3576 | |
| 3577 |
999 WRITE(6,*) 'GETPRFQ: NON CONVERGENCE IN PRESSURE' |
| 3578 |
WRITE(6,*) ' T = ', TIME
|
| 3579 |
WRITE(6,*) ' I = ', I
|
| 3580 |
WRITE(6,*) ' P = ', P(I), ' PMIN = ', PMIN(I)
|
| 3581 |
WRITE(6,*) ' R = ', R(I), ' M = ', M(I)
|
| 3582 |
WRITE(6,*) ' E = ', E(I)
|
| 3583 |
WRITE(6,*) ' VEL = ', VEL(I)
|
| 3584 |
STOP
|
| 3585 | |
| 3586 |
1000 CONTINUE |
| 3587 | |
| 3588 |
RETURN
|
| 3589 |
END
|