A Lattice Kinetic Scheme with Grid Refinement for 3 D Resistive Magnetohydrodynamics

Title A Lattice Kinetic Scheme with Grid Refinement for 3D Resistive Magnetohydrodynamics Candidate Bryan R. Osborn Degree and Year Master of Science, 2004 Thesis Committee William D. Dorland, Chair Assistant Professor of Physics Adil B. Hassam Professor of Physics C. David Levermore Professor of Mathematics We develop, analyze, and numerically test a 3D lattice kinetic scheme for the resistive magnetohydrodynamic (MHD) equations. This scheme is based on the square D3Q19 lattice for the fluid and the square D3Q7 lattice for the magnetic field. The scheme is shown to be consistent with the MHD equations in the low-Mach, high-β limit. We numerically test the scheme in a pseudo-3D implementation by examining its reproduction of linear MHD eigenmodes as well as its performance on the non-linear Orszag-Tang problem. Results show that the waves are correctly reproduced and that the code has second-order convergence in time step and grid spacing. A multi-block refinement algorithm is then tested, and its convergence properties are examined for the non-linear Orszag-Tang problem. We conclude that this multi-block refinement algorithm—previously only applied to hydrodynamic lattice kinetic schemes—can be used in conjunction with MHD lattice kinetic schemes. A Lattice Kinetic Scheme with Grid Refinement for 3D Resistive Magnetohydrodynamics