A magic two-relaxation-time lattice Boltzmann algorithm for magnetohydrodynamics

The two-relaxation-time collision operator in discrete kinetic theory models collisions between particles by grouping them into pairs with anti-parallel velocities. It prescribes a linear relaxation towards equilibrium one rate for the even combination of distribution functions each pair, and another odd combination. We reformulate this using rates forward-propagating backward-propagating combinations instead. An optimal pair sets distributions to equilibrium. Only non-equilibrium remain. Applying result twice gives closed equations evolving macroscopic variables alone across three time levels. split equivalent first-order system: conservation law equation flux. All other quantities are evaluated at apply formalism magnetic field lattice Boltzmann scheme magnetohydrodynamics. antisymmetric part matches Maxwell–Faraday Ohm's law. symmetric hyperbolic divergence cleaning model. remains zero, within round-off error, when initial is curl vector potential. have thus constructed mimetic or constrained transport