An implicit lattice Boltzmann method for simulations of compressible plasma kinetics

In this paper, an implicit lattice Boltzmann method (LBM) to speed up the simulations of compressible plasma kinetics is presented. The Boltzmann Bhatnagar-Gross-Krook equations and magnetohydrodynamics equations are used to construct a plasma simulation model. The implicit LBM needs to solve the mesoscopic equation and the macroscopic equations in each time step. The equilibrium stage distribution function and the electromagnetic force term at next time step can be predicted, by solving the macroscopic equations implicitly. Both the macroscopic and mesoscopic implicit equations are solved by using the lower-upper symmetric Gauss-Seidel factorization. Four numerical test cases, Riemann problem, shock reflection problem, Orszag-Tang vortex problem, and three-dimensional explosion in a box, have been performed to validate the implicit algorithm. The computational efficiency of the implicit LBM for compressible plasma flow can be improved by 8–25 times with the explicit LBM, which greatly reduces the computational cost.