LATTICE BOLTZMANN MAGNETOHYDRODYNAMICS

Lattice gas and lattice Boltzmann methods are recently developed numer ical schemes for simulating a variety of physical systems. In this pap er a new lattice Boltzmann model for modeling two-dimensional (2-D) in compressible magnetohydrodynamics (MHD) is presented. The current mode l fully utilizes the flexibility of the lattice Boltzmann method in co mparison with previous lattice gas and lattice Boltzmann MHD models, r educing the number of moving directions from 36 in other models to 12 only. To increase computational efficiency, a simple single time relax ation rule is used for collisions, which directly controls the transpo rt coefficients. The bidirectional streaming process of the particle d istribution function in this paper is similar to the original model [H . Chen and W. H. Matthaeus, Phys. Rev. Lett. 58, 1845 (1987), S. Chen et al., Phys. Rev. Lett. 67, 3776 (1991)], but has been greatly simpli fied, affording simpler implementation of boundary conditions and incr easing the feasibility of extension into a workable three-dimensional (3-D) model. Analytical expressions for the transport coefficients are presented. Also, as example cases, numerical calculation for the Hart mann flow is performed, showing a good agreement between the theoretic al prediction and numerical simulation, and a sheet-pinch simulation i s performed and compared with the results obtained with a spectral met hod.