| 1 |
C ------------ |
| 2 |
CN NAME: R I E M A N N |
| 3 |
C ------------ |
| 4 | |
| 5 |
CP PURPOSE: |
| 6 |
CP THIS PROGRAM COMPUTES THE SOLUTION OF A 1D |
| 7 |
CP RELATIVISTIC RIEMANN PROBLEM (FOR CONSTANT-GAMMA IDEAL GASES) WITH |
| 8 |
CP INITIAL DATA UL IF X<0.5 AND UR IF X>0.5 |
| 9 |
CP IN THE WHOLE SPATIAL DOMAIN [0, 1] |
| 10 |
C |
| 11 | |
| 12 |
CC COMMENTS: |
| 13 |
CC SEE MARTI AND MUELLER, JFM, 1994 |
| 14 |
CC |
| 15 |
CC WRITTEN BY: Jose-Maria Marti |
| 16 |
CC Departamento de Astronomia y Astrofisica |
| 17 |
CC Universidad de Valencia |
| 18 |
CC 46100 Burjassot (Valencia), Spain |
| 19 |
CC jose-maria.marti@uv.es |
| 20 |
CC AND |
| 21 |
CC Ewald Mueller |
| 22 |
CC Max-Planck-Institut fuer Astrophysik |
| 23 |
CC Karl-Schwarzschild-Str. 1 |
| 24 |
CC 85741 Garching, Germany |
| 25 |
CC emueller@mpa-garching.mpg.de |
| 26 |
C |
| 27 | |
| 28 |
PROGRAM RIEMANN
|
| 29 | |
| 30 |
IMPLICIT NONE
|
| 31 | |
| 32 |
C ------- |
| 33 |
C COMMON BLOCKS |
| 34 |
C ------- |
| 35 | |
| 36 |
DOUBLE PRECISION RHOL, PL, UL, HL, CSL, VELL, WL,
|
| 37 |
& RHOR, PR, UR, HR, CSR, VELR, WR |
| 38 |
COMMON /STATES/ RHOL, PL, UL, HL, CSL, VELL, WL,
|
| 39 |
& RHOR, PR, UR, HR, CSR, VELR, WR |
| 40 | |
| 41 |
DOUBLE PRECISION RHOLS, ULS, HLS, CSLS, VELLS, VSHOCKL
|
| 42 |
COMMON /LS/ RHOLS, ULS, HLS, CSLS, VELLS, VSHOCKL
|
| 43 | |
| 44 |
DOUBLE PRECISION RHORS, URS, HRS, CSRS, VELRS, VSHOCKR
|
| 45 |
COMMON /RS/ RHORS, URS, HRS, CSRS, VELRS, VSHOCKR
|
| 46 | |
| 47 |
DOUBLE PRECISION GAMMA
|
| 48 |
COMMON /ADIND/ GAMMA
|
| 49 | |
| 50 |
C --------- |
| 51 |
C INTERNAL VARIABLES |
| 52 |
C --------- |
| 53 | |
| 54 |
INTEGER MN, N, I, ILOOP
|
| 55 |
PARAMETER (MN = 400)
|
| 56 | |
| 57 |
DOUBLE PRECISION TOL, PMIN, PMAX, DVEL1, DVEL2, CHECK
|
| 58 | |
| 59 |
DOUBLE PRECISION PS, VELS
|
| 60 | |
| 61 |
DOUBLE PRECISION RHOA(MN), PA(MN), VELA(MN), UA(MN)
|
| 62 | |
| 63 |
DOUBLE PRECISION XI
|
| 64 | |
| 65 |
DOUBLE PRECISION RAD(MN), X1, X2, X3, X4, X5, T
|
| 66 | |
| 67 |
C ------- |
| 68 |
C INITIAL STATES |
| 69 |
C ------- |
| 70 | |
| 71 |
WRITE(*,*) ' ADIABATIC INDEX OF THE GAS: '
|
| 72 |
READ (*,*) GAMMA
|
| 73 | |
| 74 |
WRITE(*,*) ' TIME FOR THE SOLUTION: '
|
| 75 |
READ (*,*) T
|
| 76 | |
| 77 |
C ----- |
| 78 |
C LEFT STATE |
| 79 |
C ----- |
| 80 | |
| 81 |
WRITE(*,*) ' -- LEFT STATE -- '
|
| 82 |
WRITE(*,*) ' PRESSURE : '
|
| 83 |
READ (*,*) PL
|
| 84 |
WRITE(*,*) ' DENSITY : '
|
| 85 |
READ (*,*) RHOL
|
| 86 |
WRITE(*,*) ' FLOW VELOCITY: '
|
| 87 |
READ (*,*) VELL
|
| 88 | |
| 89 |
C ------ |
| 90 |
C RIGHT STATE |
| 91 |
C ------ |
| 92 | |
| 93 |
WRITE(*,*) ' -- RIGHT STATE -- '
|
| 94 |
WRITE(*,*) ' PRESSURE : '
|
| 95 |
READ (*,*) PR
|
| 96 |
WRITE(*,*) ' DENSITY : '
|
| 97 |
READ (*,*) RHOR
|
| 98 |
WRITE(*,*) ' FLOW VELOCITY: '
|
| 99 |
READ (*,*) VELR
|
| 100 | |
| 101 |
C ------------------------------ |
| 102 |
C SPECIFIC INTERNAL ENERGY, SPECIFIC ENTHALPY, SOUND SPEED AND |
| 103 |
C FLOW LORENTZ FACTORS IN THE INITIAL STATES |
| 104 |
C ------------------------------ |
| 105 | |
| 106 |
UL = PL/(GAMMA-1.D0)/RHOL
|
| 107 |
UR = PR/(GAMMA-1.D0)/RHOR
|
| 108 | |
| 109 |
HL = 1.D0+UL+PL/RHOL
|
| 110 |
HR = 1.D0+UR+PR/RHOR
|
| 111 | |
| 112 |
CSL = DSQRT(GAMMA*PL/RHOL/HL)
|
| 113 |
CSR = DSQRT(GAMMA*PR/RHOR/HR)
|
| 114 | |
| 115 |
WL = 1.D0/DSQRT(1.D0-VELL**2)
|
| 116 |
WR = 1.D0/DSQRT(1.D0-VELR**2)
|
| 117 | |
| 118 |
C -------- |
| 119 |
C NUMBER OF POINTS |
| 120 |
C -------- |
| 121 | |
| 122 |
N = 400
|
| 123 | |
| 124 |
C ------------- |
| 125 |
C TOLERANCE FOR THE SOLUTION |
| 126 |
C ------------- |
| 127 | |
| 128 |
TOL = 0.D0
|
| 129 | |
| 130 |
C |
| 131 | |
| 132 |
ILOOP = 0
|
| 133 | |
| 134 |
PMIN = (PL + PR)/2.D0
|
| 135 |
PMAX = PMIN
|
| 136 | |
| 137 |
5 ILOOP = ILOOP + 1 |
| 138 | |
| 139 |
PMIN = 0.5D0*MAX(PMIN,0.D0)
|
| 140 |
PMAX = 2.D0*PMAX
|
| 141 | |
| 142 |
CALL GETDVEL(PMIN, DVEL1)
|
| 143 | |
| 144 |
CALL GETDVEL(PMAX, DVEL2)
|
| 145 | |
| 146 |
CHECK = DVEL1*DVEL2
|
| 147 |
IF (CHECK.GT.0.D0) GOTO 5
|
| 148 | |
| 149 |
C --------------------------- |
| 150 |
C PRESSURE AND FLOW VELOCITY IN THE INTERMEDIATE STATES |
| 151 |
C --------------------------- |
| 152 | |
| 153 |
CALL GETP(PMIN, PMAX, TOL, PS)
|
| 154 | |
| 155 |
VELS = 0.5D0*(VELLS + VELRS)
|
| 156 | |
| 157 |
C --------------- |
| 158 |
C SOLUTION ON THE NUMERICAL MESH |
| 159 |
C --------------- |
| 160 | |
| 161 |
C ----------- |
| 162 |
C POSITIONS OF THE WAVES |
| 163 |
C ----------- |
| 164 | |
| 165 |
IF (PL.GE.PS) THEN
|
| 166 | |
| 167 |
X1 = 0.5D0 + (VELL - CSL)/(1.D0 - VELL*CSL)*T
|
| 168 |
X2 = 0.5D0 + (VELS - CSLS)/(1.D0 - VELS*CSLS)*T
|
| 169 | |
| 170 |
ELSE
|
| 171 | |
| 172 |
X1 = 0.5D0 + VSHOCKL*T
|
| 173 |
X2 = X1
|
| 174 | |
| 175 |
END IF
|
| 176 | |
| 177 |
X3 = 0.5D0 + VELS*T
|
| 178 | |
| 179 |
IF (PR.GE.PS) THEN
|
| 180 | |
| 181 |
X4 = 0.5D0 + (VELS + CSRS)/(1.D0 + VELS*CSRS)*T
|
| 182 |
X5 = 0.5D0 + (VELR + CSR)/(1.D0 + VELR*CSR)*T
|
| 183 | |
| 184 |
ELSE
|
| 185 | |
| 186 |
X4 = 0.5D0 + VSHOCKR*T
|
| 187 |
X5 = X4
|
| 188 | |
| 189 |
END IF
|
| 190 | |
| 191 |
C ---------- |
| 192 |
C SOLUTION ON THE MESH |
| 193 |
C ---------- |
| 194 | |
| 195 |
DO 100 I=1,N
|
| 196 | |
| 197 |
RAD(I) = DFLOAT(I)/DFLOAT(N)
|
| 198 | |
| 199 |
100 CONTINUE |
| 200 | |
| 201 |
DO 120 I=1,N
|
| 202 | |
| 203 |
IF (RAD(I).LE.X1) THEN
|
| 204 | |
| 205 |
PA(I) = PL
|
| 206 |
RHOA(I) = RHOL
|
| 207 |
VELA(I) = VELL
|
| 208 |
UA(I) = UL
|
| 209 | |
| 210 |
ELSE IF (RAD(I).LE.X2) THEN
|
| 211 | |
| 212 |
XI = (RAD(I) - 0.5D0)/T
|
| 213 | |
| 214 |
CALL RAREF(XI, RHOL, PL, UL, CSL, VELL, 'L',
|
| 215 |
& RHOA(I), PA(I), UA(I), VELA(I)) |
| 216 | |
| 217 |
ELSE IF (RAD(I).LE.X3) THEN
|
| 218 | |
| 219 |
PA(I) = PS
|
| 220 |
RHOA(I) = RHOLS
|
| 221 |
VELA(I) = VELS
|
| 222 |
UA(I) = ULS
|
| 223 | |
| 224 |
ELSE IF (RAD(I).LE.X4) THEN
|
| 225 | |
| 226 |
PA(I) = PS
|
| 227 |
RHOA(I) = RHORS
|
| 228 |
VELA(I) = VELS
|
| 229 |
UA(I) = URS
|
| 230 | |
| 231 |
ELSE IF (RAD(I).LE.X5) THEN
|
| 232 | |
| 233 |
XI = (RAD(I) - 0.5D0)/T
|
| 234 | |
| 235 |
CALL RAREF(XI, RHOR, PR, UR, CSR, VELR, 'R',
|
| 236 |
& RHOA(I), PA(I), UA(I), VELA(I)) |
| 237 | |
| 238 |
ELSE
|
| 239 | |
| 240 |
PA(I) = PR
|
| 241 |
RHOA(I) = RHOR
|
| 242 |
VELA(I) = VELR
|
| 243 |
UA(I) = UR
|
| 244 | |
| 245 |
END IF
|
| 246 | |
| 247 |
120 CONTINUE |
| 248 | |
| 249 |
OPEN (3,FILE='solution.dat',FORM='FORMATTED',STATUS='NEW')
|
| 250 | |
| 251 |
WRITE(3,150) N, T
|
| 252 |
150 FORMAT(I5,1X,F10.5) |
| 253 | |
| 254 |
DO 60 I=1,N
|
| 255 |
WRITE(3,200) RAD(I),PA(I),RHOA(I),VELA(I),UA(I)
|
| 256 |
60 CONTINUE |
| 257 | |
| 258 |
200 FORMAT(5(E15.8,1X)) |
| 259 | |
| 260 |
CLOSE(3)
|
| 261 | |
| 262 |
STOP
|
| 263 |
END
|
| 264 | |
| 265 |
C ---------- |
| 266 |
CN NAME: G E T D V E L |
| 267 |
C ---------- |
| 268 | |
| 269 |
CP PURPOSE: |
| 270 |
CP COMPUTE THE DIFFERENCE IN FLOW SPEED BETWEEN LEFT AND RIGHT INTERMEDIATE |
| 271 |
CP STATES FOR GIVEN LEFT AND RIGHT STATES AND PRESSURE |
| 272 |
C |
| 273 | |
| 274 |
CC COMMENTS |
| 275 |
CC NONE |
| 276 | |
| 277 |
SUBROUTINE GETDVEL( P, DVEL)
|
| 278 | |
| 279 |
IMPLICIT NONE
|
| 280 | |
| 281 |
C ----- |
| 282 |
C ARGUMENTS |
| 283 |
C ----- |
| 284 | |
| 285 |
DOUBLEPRECISION P, DVEL
|
| 286 | |
| 287 |
C ------- |
| 288 |
C COMMON BLOCKS |
| 289 |
C ------- |
| 290 | |
| 291 |
DOUBLE PRECISION RHOLS,ULS,HLS,CSLS,VELLS,VSHOCKL
|
| 292 |
COMMON /LS/ RHOLS,ULS,HLS,CSLS,VELLS,VSHOCKL
|
| 293 | |
| 294 |
DOUBLE PRECISION RHORS,URS,HRS,CSRS,VELRS,VSHOCKR
|
| 295 |
COMMON /RS/ RHORS,URS,HRS,CSRS,VELRS,VSHOCKR
|
| 296 | |
| 297 |
DOUBLE PRECISION RHOL, PL, UL, HL, CSL, VELL, WL,
|
| 298 |
& RHOR, PR, UR, HR, CSR, VELR, WR |
| 299 |
COMMON /STATES/ RHOL, PL, UL, HL, CSL, VELL, WL,
|
| 300 |
& RHOR, PR, UR, HR, CSR, VELR, WR |
| 301 | |
| 302 |
DOUBLE PRECISION GAMMA
|
| 303 |
COMMON /ADIND/ GAMMA
|
| 304 | |
| 305 |
C ----- |
| 306 |
C LEFT WAVE |
| 307 |
C ----- |
| 308 | |
| 309 |
CALL GETVEL(P, RHOL, PL, UL, HL, CSL, VELL, WL, 'L',
|
| 310 |
& RHOLS, ULS, HLS, CSLS, VELLS, VSHOCKL) |
| 311 | |
| 312 |
C ----- |
| 313 |
C RIGHT WAVE |
| 314 |
C ----- |
| 315 | |
| 316 |
CALL GETVEL(P, RHOR, PR, UR, HR, CSR, VELR, WR, 'R',
|
| 317 |
& RHORS, URS, HRS, CSRS, VELRS, VSHOCKR) |
| 318 | |
| 319 |
DVEL = VELLS - VELRS
|
| 320 | |
| 321 |
RETURN
|
| 322 |
END
|
| 323 | |
| 324 |
C ------- |
| 325 |
CN NAME: G E T P |
| 326 |
C ------- |
| 327 | |
| 328 |
CP PURPOSE: |
| 329 |
CP FIND THE PRESSURE IN THE INTERMEDIATE STATE OF A RIEMANN PROBLEM IN |
| 330 |
CP RELATIVISTIC HYDRODYNAMICS |
| 331 |
C |
| 332 | |
| 333 |
CC COMMENTS: |
| 334 |
CC THIS ROUTINE USES A COMBINATION OF INTERVAL BISECTION AND INVERSE |
| 335 |
CC QUADRATIC INTERPOLATION TO FIND THE ROOT IN A SPECIFIED INTERVAL. |
| 336 |
CC IT IS ASSUMED THAT DVEL(PMIN) AND DVEL(PMAX) HAVE OPPOSITE SIGNS WITHOUT |
| 337 |
CC A CHECK. |
| 338 |
CC ADAPTED FROM "COMPUTER METHODS FOR MATHEMATICAL COMPUTATION", |
| 339 |
CC BY G. E. FORSYTHE, M. A. MALCOLM, AND C. B. MOLER, |
| 340 |
CC PRENTICE-HALL, ENGLEWOOD CLIFFS N.J. |
| 341 |
C |
| 342 |
SUBROUTINE GETP( PMIN, PMAX, TOL, PS)
|
| 343 | |
| 344 |
IMPLICIT NONE
|
| 345 | |
| 346 |
C ----- |
| 347 |
C ARGUMENTS |
| 348 |
C ----- |
| 349 | |
| 350 |
DOUBLEPRECISION PMIN, PMAX, TOL, PS
|
| 351 | |
| 352 |
C ------- |
| 353 |
C COMMON BLOCKS |
| 354 |
C ------- |
| 355 | |
| 356 |
DOUBLEPRECISION GAMMA
|
| 357 |
COMMON /ADIND/ GAMMA
|
| 358 | |
| 359 |
DOUBLEPRECISION RHOL, PL, UL, HL, CSL, VELL, WL,
|
| 360 |
& RHOR, PR, UR, HR, CSR, VELR, WR |
| 361 |
COMMON /STATES/ RHOL, PL, UL, HL, CSL, VELL, WL,
|
| 362 |
& RHOR, PR, UR, HR, CSR, VELR, WR |
| 363 | |
| 364 |
C --------- |
| 365 |
C INTERNAL VARIABLES |
| 366 |
C --------- |
| 367 | |
| 368 |
DOUBLEPRECISION A, B, C, D, E, EPS, FA, FB, FC, TOL1,
|
| 369 |
& XM, P, Q, R, S |
| 370 | |
| 371 |
C ------------- |
| 372 |
C COMPUTE MACHINE PRECISION |
| 373 |
C ------------- |
| 374 | |
| 375 |
EPS = 1.D0
|
| 376 |
10 EPS = EPS/2.D0 |
| 377 |
TOL1 = 1.D0 + EPS
|
| 378 |
IF( TOL1 .GT. 1.D0) GO TO 10
|
| 379 | |
| 380 |
C ------- |
| 381 |
C INITIALIZATION |
| 382 |
C ------- |
| 383 | |
| 384 |
A = PMIN
|
| 385 |
B = PMAX
|
| 386 |
CALL GETDVEL(A,FA)
|
| 387 |
CALL GETDVEL(B,FB)
|
| 388 | |
| 389 |
C ----- |
| 390 |
C BEGIN STEP |
| 391 |
C ----- |
| 392 | |
| 393 |
20 C = A |
| 394 |
FC = FA
|
| 395 |
D = B - A
|
| 396 |
E = D
|
| 397 |
30 IF( DABS(FC) .GE. DABS(FB))GO TO 40 |
| 398 |
A = B
|
| 399 |
B = C
|
| 400 |
C = A
|
| 401 |
FA = FB
|
| 402 |
FB = FC
|
| 403 |
FC = FA
|
| 404 | |
| 405 |
C -------- |
| 406 |
C CONVERGENCE TEST |
| 407 |
C -------- |
| 408 | |
| 409 |
40 TOL1 = 2.D0*EPS*DABS(B) + 0.5D0*TOL |
| 410 |
XM = 0.5D0*(C - B)
|
| 411 |
IF( DABS(XM) .LE. TOL1) GO TO 90
|
| 412 |
IF( FB .EQ. 0.D0) GO TO 90
|
| 413 | |
| 414 |
C ------------ |
| 415 |
C IS BISECTION NECESSARY? |
| 416 |
C ------------ |
| 417 | |
| 418 |
IF( DABS(E) .LT. TOL1) GO TO 70
|
| 419 |
IF( DABS(FA) .LE. DABS(FB)) GO TO 70
|
| 420 | |
| 421 |
C ------------------ |
| 422 |
C IS QUADRATIC INTERPOLATION POSSIBLE? |
| 423 |
C ------------------ |
| 424 | |
| 425 |
IF( A .NE. C) GO TO 50
|
| 426 | |
| 427 |
C ---------- |
| 428 |
C LINEAR INTERPOLATION |
| 429 |
C ---------- |
| 430 | |
| 431 |
S = FB/FA
|
| 432 |
P = 2.D0*XM*S
|
| 433 |
Q = 1.D0 - S
|
| 434 |
GO TO 60
|
| 435 | |
| 436 |
C ---------------- |
| 437 |
C INVERSE QUADRATIC INTERPOLATION |
| 438 |
C ---------------- |
| 439 | |
| 440 |
50 Q = FA/FC |
| 441 |
R = FB/FC
|
| 442 |
S = FB/FA
|
| 443 |
P = S*(2.D0*XM*Q*(Q - R) - (B - A)*(R - 1.D0))
|
| 444 |
Q = (Q - 1.D0)*(R - 1.D0)*(S - 1.D0)
|
| 445 | |
| 446 |
C ------ |
| 447 |
C ADJUST SIGNS |
| 448 |
C ------ |
| 449 | |
| 450 |
60 IF( P .GT. 0.D0) Q = -Q |
| 451 |
P = DABS(P)
|
| 452 | |
| 453 |
C -------------- |
| 454 |
C IS INTERPOLATION ACCEPTABLE? |
| 455 |
C -------------- |
| 456 | |
| 457 |
IF( (2.D0*P) .GE. (3.D0*XM*Q-DABS(TOL1*Q))) GO TO 70
|
| 458 |
IF( P .GE. DABS(0.5D0*E*Q)) GO TO 70
|
| 459 |
E = D
|
| 460 |
D = P/Q
|
| 461 |
GO TO 80
|
| 462 | |
| 463 |
C ----- |
| 464 |
C BISECTION |
| 465 |
C ----- |
| 466 | |
| 467 |
70 D = XM |
| 468 |
E = D
|
| 469 | |
| 470 |
C ------- |
| 471 |
C COMPLETE STEP |
| 472 |
C ------- |
| 473 | |
| 474 |
80 A = B |
| 475 |
FA = FB
|
| 476 |
IF( DABS(D) .GT. TOL1) B = B+D
|
| 477 |
IF( DABS(D) .LE. TOL1) B = B+DSIGN(TOL1,XM)
|
| 478 |
CALL GETDVEL(B,FB)
|
| 479 |
IF( (FB*(FC/DABS(FC))) .GT. 0.D0) GO TO 20
|
| 480 |
GO TO 30
|
| 481 | |
| 482 |
C -- |
| 483 |
C DONE |
| 484 |
C -- |
| 485 | |
| 486 |
90 PS = B |
| 487 | |
| 488 |
RETURN
|
| 489 |
END
|
| 490 | |
| 491 |
C --------- |
| 492 |
CN NAME: G E T V E L |
| 493 |
C --------- |
| 494 | |
| 495 |
CP PURPOSE: |
| 496 |
CP COMPUTE THE FLOW VELOCITY BEHIND A RAREFACTION OR SHOCK IN TERMS OF THE |
| 497 |
CP POST-WAVE PRESSURE FOR A GIVEN STATE AHEAD THE WAVE IN A RELATIVISTIC |
| 498 |
CP FLOW |
| 499 |
C |
| 500 | |
| 501 |
CC COMMENTS: |
| 502 |
CC THIS ROUTINE CLOSELY FOLLOWS THE EXPRESSIONS IN MARTI AND MUELLER, |
| 503 |
CC J. FLUID MECH., (1994) |
| 504 | |
| 505 |
SUBROUTINE GETVEL( P, RHOA, PA, UA, HA, CSA, VELA, WA, S,
|
| 506 |
& RHO, U, H, CS, VEL, VSHOCK) |
| 507 | |
| 508 |
IMPLICIT NONE
|
| 509 | |
| 510 |
C ----- |
| 511 |
C ARGUMENTS |
| 512 |
C ----- |
| 513 | |
| 514 |
DOUBLE PRECISION P, RHOA, PA, UA, HA, CSA, VELA, WA
|
| 515 |
CHARACTER*1 S
|
| 516 |
DOUBLE PRECISION RHO, U, H, CS, VEL, VSHOCK
|
| 517 | |
| 518 |
C ------- |
| 519 |
C COMMON BLOCKS |
| 520 |
C ------- |
| 521 | |
| 522 |
DOUBLE PRECISION GAMMA
|
| 523 |
COMMON /ADIND/ GAMMA
|
| 524 | |
| 525 |
C --------- |
| 526 |
C INTERNAL VARIABLES |
| 527 |
C --------- |
| 528 | |
| 529 |
DOUBLE PRECISION A, B, C, SIGN
|
| 530 |
DOUBLE PRECISION J, WSHOCK
|
| 531 |
DOUBLE PRECISION K, SQGL1
|
| 532 | |
| 533 |
C --------------- |
| 534 |
C LEFT OR RIGHT PROPAGATING WAVE |
| 535 |
C --------------- |
| 536 | |
| 537 |
IF (S.EQ.'L') SIGN = -1.D0
|
| 538 | |
| 539 |
IF (S.EQ.'R') SIGN = 1.D0
|
| 540 | |
| 541 |
C |
| 542 | |
| 543 |
IF (P.GT.PA) THEN
|
| 544 | |
| 545 |
C --- |
| 546 |
C SHOCK |
| 547 |
C --- |
| 548 | |
| 549 |
A = 1.D0+(GAMMA-1.D0)*(PA-P)/GAMMA/P
|
| 550 |
B = 1.D0-A
|
| 551 |
C = HA*(PA-P)/RHOA-HA**2
|
| 552 | |
| 553 |
C ---------------- |
| 554 |
C CHECK FOR UNPHYSICAL ENTHALPIES |
| 555 |
C ---------------- |
| 556 | |
| 557 |
IF (C.GT.(B**2/4.D0/A)) STOP
|
| 558 |
& 'GETVEL: UNPHYSICAL SPECIFIC ENTHALPY IN INTERMEDIATE STATE' |
| 559 | |
| 560 |
C ----------------------------- |
| 561 |
C SPECIFIC ENTHALPY IN THE POST-WAVE STATE |
| 562 |
C (FROM THE EQUATION OF STATE AND THE TAUB ADIABAT, |
| 563 |
C EQ.(74), MM94) |
| 564 |
C ----------------------------- |
| 565 | |
| 566 |
H = (-B+DSQRT(B**2-4.D0*A*C))/2.D0/A
|
| 567 | |
| 568 |
C --------------- |
| 569 |
C DENSITY IN THE POST-WAVE STATE |
| 570 |
C (FROM EQ.(73), MM94) |
| 571 |
C --------------- |
| 572 | |
| 573 |
RHO = GAMMA*P/(GAMMA-1.D0)/(H-1.D0)
|
| 574 | |
| 575 |
C ------------------------ |
| 576 |
C SPECIFIC INTERNAL ENERGY IN THE POST-WAVE STATE |
| 577 |
C (FROM THE EQUATION OF STATE) |
| 578 |
C ------------------------ |
| 579 | |
| 580 |
U = P/(GAMMA-1.D0)/RHO
|
| 581 | |
| 582 |
C -------------------------- |
| 583 |
C MASS FLUX ACROSS THE WAVE |
| 584 |
C (FROM THE RANKINE-HUGONIOT RELATIONS, EQ.(71), MM94) |
| 585 |
C -------------------------- |
| 586 | |
| 587 |
J = SIGN*DSQRT((P-PA)/(HA/RHOA-H/RHO))
|
| 588 | |
| 589 |
C ---------- |
| 590 |
C SHOCK VELOCITY |
| 591 |
C (FROM EQ.(86), MM94 |
| 592 |
C ---------- |
| 593 | |
| 594 |
A = J**2+(RHOA*WA)**2
|
| 595 |
B = -VELA*RHOA**2*WA**2
|
| 596 |
VSHOCK = (-B+SIGN*J**2*DSQRT(1.D0+RHOA**2/J**2))/A
|
| 597 |
WSHOCK = 1.D0/DSQRT(1.D0-VSHOCK**2)
|
| 598 | |
| 599 |
C ------------------- |
| 600 |
C FLOW VELOCITY IN THE POST-SHOCK STATE |
| 601 |
C (FROM EQ.(67), MM94) |
| 602 |
C ------------------- |
| 603 | |
| 604 |
A = WSHOCK*(P-PA)/J+HA*WA*VELA
|
| 605 |
B = HA*WA+(P-PA)*(WSHOCK*VELA/J+1.D0/RHOA/WA)
|
| 606 | |
| 607 |
VEL = A/B
|
| 608 | |
| 609 |
C --------------------- |
| 610 |
C LOCAL SOUND SPEED IN THE POST-SHOCK STATE |
| 611 |
C (FROM THE EQUATION OF STATE) |
| 612 |
C --------------------- |
| 613 | |
| 614 |
CS = DSQRT(GAMMA*P/RHO/H)
|
| 615 | |
| 616 |
ELSE
|
| 617 | |
| 618 |
C ------ |
| 619 |
C RAREFACTION |
| 620 |
C ------ |
| 621 | |
| 622 |
C --------------------------- |
| 623 |
C POLITROPIC CONSTANT OF THE GAS ACROSS THE RAREFACTION |
| 624 |
C --------------------------- |
| 625 | |
| 626 |
K = PA/RHOA**GAMMA
|
| 627 | |
| 628 |
C --------------- |
| 629 |
C DENSITY BEHIND THE RAREFACTION |
| 630 |
C --------------- |
| 631 | |
| 632 |
RHO = (P/K)**(1.D0/GAMMA)
|
| 633 | |
| 634 |
C ------------------------ |
| 635 |
C SPECIFIC INTERNAL ENERGY BEHIND THE RAREFACTION |
| 636 |
C (FROM THE EQUATION OF STATE) |
| 637 |
C ------------------------ |
| 638 | |
| 639 |
U = P/(GAMMA-1.D0)/RHO
|
| 640 | |
| 641 |
C -------------------- |
| 642 |
C LOCAL SOUND SPEED BEHIND THE RAREFACTION |
| 643 |
C (FROM THE EQUATION OF STATE) |
| 644 |
C -------------------- |
| 645 | |
| 646 |
CS = DSQRT(GAMMA*P/(RHO+GAMMA*P/(GAMMA-1.D0)))
|
| 647 | |
| 648 |
C ------------------ |
| 649 |
C FLOW VELOCITY BEHIND THE RAREFACTION |
| 650 |
C ------------------ |
| 651 | |
| 652 |
SQGL1 = DSQRT(GAMMA-1.D0)
|
| 653 |
A = (1.D0+VELA)/(1.D0-VELA)*
|
| 654 |
& ((SQGL1+CSA)/(SQGL1-CSA)* |
| 655 |
& (SQGL1-CS)/(SQGL1+CS))**(-SIGN*2.D0/SQGL1) |
| 656 | |
| 657 |
VEL = (A-1.D0)/(A+1.D0)
|
| 658 | |
| 659 |
END IF
|
| 660 | |
| 661 |
END
|
| 662 | |
| 663 |
C -------- |
| 664 |
CN NAME: R A R E F |
| 665 |
C -------- |
| 666 | |
| 667 |
CP PURPOSE: |
| 668 |
CP COMPUTE THE FLOW STATE IN A RAREFACTION FOR GIVEN PRE-WAVE STATE |
| 669 |
C |
| 670 | |
| 671 |
CC COMMENTS: |
| 672 |
CC THIS ROUTINE CLOSELY FOLLOWS THE EXPRESSIONS IN MARTI AND MUELLER, |
| 673 |
CC J. FLUID MECH., (1994) |
| 674 | |
| 675 |
SUBROUTINE RAREF( XI, RHOA, PA, UA, CSA, VELA, S, RHO, P, U, VEL)
|
| 676 | |
| 677 |
IMPLICIT NONE
|
| 678 | |
| 679 |
C ----- |
| 680 |
C ARGUMENTS |
| 681 |
C ----- |
| 682 | |
| 683 |
DOUBLE PRECISION XI
|
| 684 | |
| 685 |
DOUBLE PRECISION RHOA, PA, UA, CSA, VELA
|
| 686 | |
| 687 |
CHARACTER S
|
| 688 | |
| 689 |
DOUBLE PRECISION RHO, P, U, VEL
|
| 690 | |
| 691 |
C ------- |
| 692 |
C COMMON BLOCKS |
| 693 |
C ------- |
| 694 | |
| 695 |
DOUBLE PRECISION GAMMA
|
| 696 |
COMMON /ADIND/ GAMMA
|
| 697 | |
| 698 |
C --------- |
| 699 |
C INTERNAL VARIABLES |
| 700 |
C --------- |
| 701 | |
| 702 |
DOUBLE PRECISION B, C, D, K, L, V, OCS2, FCS2, DFDCS2, CS2, SIGN
|
| 703 | |
| 704 |
C --------------- |
| 705 |
C LEFT OR RIGHT PROPAGATING WAVE |
| 706 |
C --------------- |
| 707 | |
| 708 |
IF (S.EQ.'L') SIGN = 1.D0
|
| 709 | |
| 710 |
IF (S.EQ.'R') SIGN = -1.D0
|
| 711 | |
| 712 |
B = DSQRT(GAMMA - 1.D0)
|
| 713 |
C = (B + CSA)/(B - CSA)
|
| 714 |
D = -SIGN*B/2.D0
|
| 715 |
K = (1.D0 + XI)/(1.D0 - XI)
|
| 716 |
L = C*K**D
|
| 717 |
V = ((1.D0 - VELA)/(1.D0 + VELA))**D
|
| 718 | |
| 719 |
OCS2 = CSA
|
| 720 | |
| 721 |
25 FCS2 = L*V*(1.D0 + SIGN*OCS2)**D*(OCS2 - B) + |
| 722 |
& (1.D0 - SIGN*OCS2)**D*(OCS2 + B) |
| 723 | |
| 724 |
DFDCS2 = L*V*(1.D0 + SIGN*OCS2)**D*
|
| 725 |
& (1.D0 + SIGN*D*(OCS2 - B)/(1.D0 + SIGN*OCS2)) + |
| 726 |
& (1.D0 - SIGN*OCS2)**D* |
| 727 |
& (1.D0 - SIGN*D*(OCS2 + B)/(1.D0 - SIGN*OCS2)) |
| 728 | |
| 729 |
CS2 = OCS2 - FCS2/DFDCS2
|
| 730 | |
| 731 |
IF (ABS(CS2 - OCS2)/OCS2.GT.5.E-7)THEN
|
| 732 |
OCS2 = CS2
|
| 733 |
GOTO 25
|
| 734 |
END IF
|
| 735 | |
| 736 |
VEL = (XI + SIGN*CS2)/(1.D0 + SIGN*XI*CS2)
|
| 737 | |
| 738 |
RHO = RHOA*((CS2**2*(GAMMA - 1.D0 - CSA**2))/
|
| 739 |
& (CSA**2*(GAMMA - 1.D0 - CS2**2))) |
| 740 |
& **(1.D0/(GAMMA - 1.D0)) |
| 741 | |
| 742 |
P = CS2**2*(GAMMA - 1.D0)*RHO/(GAMMA - 1.D0 - CS2**2)/GAMMA
|
| 743 | |
| 744 |
U = P/(GAMMA - 1.D0)/RHO
|
| 745 | |
| 746 |
RETURN
|
| 747 |
END
|