Lattice Boltzmann Methods for Compressible Magnetohydrodynamics

Compressible, magnetised plasma flows pervade astrophysics, from stellar winds to planetary magnetospheres and the interstellar medium. Their high-fidelity simulation at scale is limited by the non-local operations that conventional solvers require for flux reconstruction, gradient and stress evaluation, and magnetic-divergence control, which bottleneck communication on heterogeneous supercomputers. We present a novel class of fully local Lattice Boltzmann Method (LBM) schemes for compressible magnetohydrodynamics (MHD) in which all nonlinear operations are point-wise. The approach exploits the kinetic structure to transport each state variable of the Strang-split conservation laws alongside its characteristics, recovering the compressible macroscopic fluxes, gradients, and viscous stresses through local relaxation rather than finite-difference stencils. Divergence control enters as a local source term within the same kinetic update, with no separate global solve. The formulation is partial-differential-equation agnostic and encompasses hydrodynamic limits such as the compressible Euler and incompressible Navier-Stokes equations. We discretise both ideal compressible and resistive incompressible MHD, and validate the scheme across multiple resolutions against the canonical astrophysical MHD test suite: the Brio-Wu shock tube resolves compound waves and slow-fast shocks, the MHD rotor captures strong torsional Alfvén waves, and the Orszag-Tang vortex reproduces current-sheet formation and the transition to MHD turbulence. Implemented in the performance-portable framework OpenLB, the scheme reaches up to 98.9 per cent of the hardware roofline on GPU. Finally, as a capability demonstration, we simulate a rotating, surface-resolved magnetised body modelled after 16 Psyche in a supersonic early solar wind, yielding an emergent bow shock, flux-rope magnetosheath, and reconnecting magnetotail.