Island Coalescence
This models an instability in a reduced 2D tokamak model. Here, we look at a thin annulus in the cross section of a large-aspect ratio tokamak. The magnetic field in the toroidal direction (going around the torus) is large and mostly constant. Therefore, we only consider the instabilities in the poloidal direction. An initial equilibrium is perturbed resulting in two peaks of current density coalescing together. The result is a reconnection of magnetic field lines and sharp spike in current density at the reconnection point. The following movies show this for a variety of parameters.

R = Reynolds Number
S = Lundquist Number
3D Parallel Results
(simulations by Lei Tang on Frost: IBM Blue Gene/L, formerly at NCAR)
2D Serial Results (Contour Plots)

Two-Phase Flow

In these experiments, we use the diffusive interface theory to model the interaction of two fluids. The two fluids are distinguished from each other by introducing a phase-function. In the diffusive mixing region, the phillic and the phobic forces compete either to bring the two fluids together or to keep them separated. Depending on the parameters of the problem, the inherent energy laws will govern the behavior of the two fluids.

Osculating Bubbles: 2 Bubbles of Fluid 1 Immersed in Fluid 2
Square to Circle: 1 Bubble of Fluid 1 Immersed in Fluid 2
Varying Viscosity in L-shaped Bubble
Bubble in Pipe
Liquid Crystals

In these experiments, we study various phenomena in static liquid cyrstal test problems. We look at varying parameters that affect the splay, twist, and bend of a liquid crystal configuration. In addition, we introduce a static electric field with and without a polarizing effect to see how the configuration changes. In all cases, we assume the liquid crystal is made up of cylindrical rods that can point in any direction, but only vary in the 2D plane and have length 1. We test how well a least-squares finite element approach does in solving such systems. The vector fields of the rods are displayed in the following movies. Here, the parameters K1, K2, and K3 represent the twist, splay, and bend Frank constants of the overall configuration.

Banana Crystals
Electric Field Added No Polarization Effect