Modeling of nonequilibrium effects in a compressible plasma based on the lattice Boltzmann method

A magnetohydrodynamic lattice Boltzmann method (MHD-LBM) model for a 2D compressible plasma based on the finite volume scheme is established. The double distribution D2Q17 discrete velocities are used to simulate the fluid field. The hyperbolic Maxwell equations, which satisfy the elliptic constraints of Maxwell's equations and the constraint of charge conservation, are used to simulate the electromagnetic field. The flow field and electromagnetic field are coupled to simulate a compressible plasma through the electromagnetic force and magnetic induction equations. Four typical cases, the Taylor vortex flow, strong blast, Orszag–Tang vortex, and one-dimensional Riemann problems, are simulated to validate the MHD-LBM model for a compressible plasma. It is found that shock waves widely exist in a compressible plasma, and strong nonequilibrium effects exist around each shock wave. The quantitative simulation for the Brio–Wu problem demonstrates that this model can easily obtain the physical characteristics of nonequilibrium effects at sharp interfaces (shock waves and detonation waves). The magnetic fields can affect the magnitudes to which the system deviates from its equilibrium state. The viscosity can increase the magnitudes to which the system deviates from its equilibrium state. Compared with existing compressible MHD, these results for nonequilibrium effects can provide mesoscopic physical insights into the flow mechanism of a shock wave in a supersonic plasma.