Lattice Boltzmann Methods for Compressible Magnetohydrodynamics
- 1Lattice Boltzmann Research Group (LBRG) , Straße am Forum 8 / Englerstraße 2, 76131 Karlsruhe ,
- 2Institute of Mechanical Process Engineering and Mechanics (MVM), Karlsruhe Institute of Technology (KIT) , Straße am Forum 8, 76131 Karlsruhe ,
- 3Institute for Applied and Numerical Mathematics (IANM), Karlsruhe Institute of Technology (KIT) , Englerstraße 2, 76131 Karlsruhe ,
Abstract
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.
Versions
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BibTeX
@article{bukreev2026lattice,
title = {{Lattice Boltzmann Methods for Compressible Magnetohydrodynamics}},
author = {Fedor Bukreev and Adrian Kummerländer and Mathias J Krause},
journal = {Monthly Notices of the Royal Astronomical Society},
year = {2026},
month = oct,
doi = {10.1093/mnras/stag1979},
url = {https://academic.oup.com/mnras/advance-article/doi/10.1093/mnras/stag1979/8943796},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Lattice Boltzmann Methods for Compressible Magnetohydrodynamics
AU - Fedor Bukreev
AU - Adrian Kummerländer
AU - Mathias J Krause
PY - 2026
DA - 2026/10/19
JO - Monthly Notices of the Royal Astronomical Society
DO - 10.1093/mnras/stag1979
UR - https://academic.oup.com/mnras/advance-article/doi/10.1093/mnras/stag1979/8943796
AB - 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.
SN - 0035-8711
SN - 1365-2966
ER -