School of Physics

James Hilton's Home Page

Computational Fluid Dynamics

Currently I'm working in the Complex Systems group in Trinity College Dublin. My research focuses on rheology models of non-Newtonian fluids and granular media. I'm using continuum models to simulate systems with various constitutive stress relations for comparison to both theory and experimental work . I'm also simulating two phase systems, such as fluid and gas systems, using the level set method.

I'm developing software for the simulation of non-Newtonian viscoelastic fluid flow, using a ‘log-conformation’ representation and using it to investigate stresses induced on objects in streams of these viscoelastic fluids. I'm also working on extensions to the level set method to include interfacial forces in complex fluids.

Here's a nice picture of a von Karman street developing behind a cylinder using my software. The Reynolds number is 10,000 for this simulation and the colour scale shows the magnitude of the velocity:

Video here, you'll need the XVid codec.

Microfluidics and Bubble Dynamics

Two phase systems, such as gases and liquids, can be modelled using the level set method, (pioneered by Sethian and Osher). The method provides a very natural way to handle the changing topology of the system as the interface is represented as the zero of a scalar level set value. This value is less than zero on one side of the interface and greater than zero on the other. This scalar obeys a simple advection expression, and the motion of the interface can easily be tracked by finding the zero value at each timestep. Another good property of the level set method is the ability to easily determine the interface curvature (as the normal of the interface is given by the gradient of the level set). This allows the addition of surface tension to the method, and so one application of this is for modelling of  bubble dynamics. At the moment I'm using this method for simulating microbubble generators. The bubble size is highly dependant on the geometry of the system, and we're currently investigating how the various parameters of the setup determine the resulting bubble dimensions. The simulation software has just been updated to handle 3D geometry, here's a cross section of the bubble generation in a microfluidic bubble generator. The system dimensions are 1cmx2cm:

3D Video here (mpg).

Video here (mpg).

Elastic Solid and Fluid Interaction

I'm also developing a way of simulating both elastic solids and liquids in the same system. This means you can do interesting things like simulate interacting particles in air currents and model sedimentation effects. Of course, the particles can be any shape, such as the 'U' shapes below. The elasticity constant can be set to a low value, to give some nice dynamics:

Video here, you'll need the XVid codec. Furthermore, the solid phase can also be determined at each timestep by the system itself, i.e. you can simulate complex liquids which have a solid phase, such as Bingham plastics. Below is a video in which the solid phase is temperature dependant, so the solid melts above a certain temperature. The square is the initial solid, and it sits on a fixed heat source. The blob that drops off behaves elastically:

Video here, you'll need the XVid codec.

Charged Droplets

Computational Magnetics

During my research I found a few new useful magnetic designs. These include a new cylindrical magnetic field source with a uniform field more homogeneous than any existing design. Some designs based on ‘flux sheets’ were also developed, which could generate either a uniform field gradient or regions of constant field and field gradient product. Several of these designs were commissioned and the computational simulations exactly agreed with the fields measured.

I developed automated finite element simulation software, using the ‘IEEE Japan’ magnetostatic vector potential formulation. The program included various optimization techniques for solving inverse design problems such as sequential golden section searches and simulated annealing etc. You can download it here, along with some scripting examples. The program also includes a new computational algorithm I developed, based on the charge model, which can calculate fields from arbitrary magnetic structures composed of hard magnetic materials. The program can handle any shapes of hard material, since it sums over the boundary surfaces.

• JF Computational Lab