A Lattice Boltzmann Model for Two-Dimensional Magnetohydrodynamics

A lattice Boltzmann model (LBM) has been developed for simulating magnetohydrodynamics (MHD) along the line of Dellar J. Comput. Phys. 179(2002)95. In this model the magnetic field is presented by a vector valued magnetic distribution function which obeys a vector Boltzmann equation. The truncated error of the equilibrium distribution in the present model is up to order O(u⁴) in velocity u rather than the usual O(u³). For verification, the model is applied to solve the shock tube problem and the main features of the flow predicted by the model are found to compare well with the corresponding results obtained with high-order semi-discrete schemes J. Comput. Phys. 201(2004)261. The numerical experiments have also shown that the present LBM model with the equilibrium distribution truncated at O(u⁴) performs much better in terms of numerical stability than those truncated at O(u³).