Lattice Boltzmann simulations 
V. Babin and R. Holyst 
The Lattice Boltzmann approach has attracted much attention recently, hence, we have also followed this direction. Using the algorithm proposed by C. Denniston, D. Marenduzzo, E. Orlandini, J. M. Yeomans, we have simulated the process of defects annihilation in nematic liquid crystals. In addition, we have also implemented the lattice Boltzmann simulator of the familiar liquid/vapor flows (see Michael R. Swift, W. R. Osborn, J. M. Yeomans). The source code can be downloaded here.
All the movies below have been encoded with MEncoder. To watch the movies, the DivX codec must be installed on your system.

Annihilation of four dislocation lines in a nematic liquid crystal. Shown is the evolution of the aligment tensor. The values of the tensor are represented by ellipsoids so that the axes of the ellipsoid are directed along the eigenvectors of the aligment tensor, while their lengths are proportional to the corresponding eigenvalues. The movie frames are rendered using POVRay. Notice the anisotropy of defects speed, which is due to the backflow. 

Spinodal decomposition of the twodimensional nonideal fluid (with the van der Waals equation of state) in the shear flow. Shown is the time evolution of the density. The redwhiteblue colourmap is used to visualize the magnitude of the fluid density. The size of the simulation box is 512x288. Periodic boundary conditions in horizontal direction are assumed. 

Spinodal decomposition of the nonideal fluid (with the van der Waals equation of state). Shown is the time evolution of the density. The light/dark blue colourmap is used to visualize the magnitude of the fluid density. The level surface, corresponding to the liquid/vapor interface, is also shown. The movie frames are rendered using OpenDX. The size of the simulation box is 160x160x160, and the periodic boundary conditions in all three dimensions are assumed. 