Computational Methods of Lattice Boltzmann Mhd

Lattice Boltzmann (LB) Methods are a somewhat novel approach to Computational Fluid Dynamics (CFD) simulations. These methods simulate Navier-Stokes and magnetohydrodynamics (MHD) equations on the mesoscopic (quasi-kinetic) scale by solving for a statistical distribution of particles rather than attempting to solve the nonlinear macroscopic equations directly. These LB methods allow for a highly parallelizable code since one replaces the difficult nonlinear convective derivatives of MHD by simple linear advection on a lattice. New developments in LB have significantly extended the numerical stability limits of its applicability. These developments include multiple relaxation times (MRT) in the collision operators, maximizing entropy to ensure positive definiteness in the distribution functions, as well as large eddy simulations of MHD turbulence. Improving the limits of this highly parallelizable simulation method allows it to become an ideal candidate for simulating various fluid and plasma problems; improving both the speed of the simulation and the spatial grid resolution of the LB algorithms on today\u27s high performance supercomputers. Some of these LB extensions are discussed and tested against various problems in magnetized plasmas