A New Lattice Boltzmann Model For Incompressible MHD Flow

In recent years, the lattice Boltzmann method (LBM) is a new numerical scheme based on kinetic theory to simulate fluid flows. Compared with traditional computational approaches, the method is simple, intrinsically parallel, and easy to incorporate complex boundary conditions. In recent years, the lattice Boltzmann method has been successfully applied into many hydro-fields, such as turbulence, porous media flow, and multiphase fluid flow, suspend particle flow, magneto hydrodynamics and so on.In this paper we proposed a new lattice Boltzmann scheme for incompressible magneto hydrodynamics flow. It is a general model suitable for both two-dimensional and three-dimensional case. The magnetic field is represented by a separate vector distribution function, which obeys a kinetic BGK-type evolution equation. Although there is no analogous microscopic process for the magnetic field, it can be argued that any conservative system can be formulated in this way under appropriate constrain. So, we use the double distribution function to denote the fluid and magnetic field respectively, to simulate the system through the two BGK equations. Besides, one parameterβwhich is restricted is added into the magnetic distribution function, so magnetic diffusion rateηis controllable and model is more general. Especially, in three dimensional, the magnetic diffusion rateηand kinetic viscosityυcould be set equal. Compared with existing models, this model is more stable, usable, easily parallel implemented without any extrapolation, less computing space. Through the numerical simulations of two-dimensional, three-dimensional Hartmann flow and Taylor-Green Vortex, the numerical results agree well with the analytic results and the numerical accuracy and stability of the schemes have been proved by these schemes correctly. Besides, we use the parallel program to simulate our model, the difference between parallel program and serial program is 10-12, less than the machine error.