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A robust and efficient solver based on kinetic schemes for Magnetohydrodynamics (MHD) equations

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  • Baty, Hubert
  • Drui, Florence
  • Helluy, Philippe
  • Franck, Emmanuel
  • Klingenberg, Christian
  • Thanhäuser, Lukas

Abstract

This paper is devoted to the simulation of compressible magnetohydrodynamic (MHD) flows with the Lattice Boltzmann Method (LBM). The usual LBM is limited to low-Mach flows. We propose a robust and accurate numerical method based on the vectorial kinetic construction of [5,25], which allows us to extend the LBM to arbitrary Mach flows. We also explain how to adjust the numerical viscosity in order to obtain stable and accurate results in smooth or discontinuous parts of the flow and reduced divergence errors. The method can handle shock waves and can be made second order in smooth regions. It is also very well adapted to computing with Graphics Processing Unit (GPU). Our GPU implementation in 2D achieves state-of-the-art accuracy, with near-optimal performance. We finally present numerical computations of a tilt instability that demonstrate the capability of the method to handle physically relevant simulations.

Suggested Citation

  • Baty, Hubert & Drui, Florence & Helluy, Philippe & Franck, Emmanuel & Klingenberg, Christian & Thanhäuser, Lukas, 2023. "A robust and efficient solver based on kinetic schemes for Magnetohydrodynamics (MHD) equations," Applied Mathematics and Computation, Elsevier, vol. 440(C).
    • Handle: RePEc:eee:apmaco:v:440:y:2023:i:c:s0096300322007263
    DOI: 10.1016/j.amc.2022.127667
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    References listed on IDEAS

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    1. Otomo, Hiroshi & Boghosian, Bruce M. & Dubois, François, 2017. "Two complementary lattice-Boltzmann-based analyses for nonlinear systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 486(C), pages 1000-1011.
    2. François Dubois, 2014. "Simulation of strong nonlinear waves with vectorial lattice Boltzmann schemes," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 25(12), pages 1-9.
    3. Matej Špeťko & Ondřej Vysocký & Branislav Jansík & Lubomír Říha, 2021. "DGX-A100 Face to Face DGX-2—Performance, Power and Thermal Behavior Evaluation," Energies, MDPI, vol. 14(2), pages 1-18, January.
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