Partial entropic stabilization of lattice Boltzmann magnetohydrodynamics

The entropic lattice Boltzmann algorithm of Karlin et al. [Phys. Rev. E 90, 031302 (2014)] is partially extended to magnetohydrodynamics, based on the Dellar model of introducing a vector distribution for the magnetic field. This entropic ansatz is now applied only to the scalar particle distribution function so as to permit the many problems entailing magnetic field reversal. A 9-bit lattice is employed for both particle and magnetic distributions for our two-dimensional simulations. The entropic ansatz is benchmarked against our earlier multiple relaxation lattice-Boltzmann model for the Kelvin-Helmholtz instability in a magnetized jet. Other two-dimensional simulations are performed and compared to results determined by more standard direct algorithms: in particular the switch over between the Kelvin-Helmholtz or tearing mode instability of Chen et al. [J. Geophys. Res.: Space Phys. 102, 151 (1997)], and the generalized Orszag-Tang vortex model of Biskamp-Welter [Phys. Fluids B 1, 1964 (1989)]. Very good results are achieved.