A kinetic method for solving the MHD equations. Application to the computation of tilt instability on uniform fine meshes

Hubert Baty (1) , Florence Drui (2) , Emmanuel Franck (3) , Philippe Helluy (3) , Christian Klingenberg (4) , Lukas Tannhaüser (4)

1 ObAS - Observatoire astronomique de Strasbourg
2 CEA - Commissariat à l'énergie atomique et aux énergies alternatives
3 TONUS - TOkamaks and NUmerical Simulations
4 University of Würzburg

This paper is devoted to the simulation of MHD flows with complex structures. This kind flows present instabilities that generate shock waves. We propose a robust and precise numerical method based on the Lattice Boltzmann methodology. We explain how to adjust the numerical viscosity in order to obtain stable, precise results and reduced divergence errors. This method can handle shock wave and is almost second order. It is also very well adapted to GPU computing. We also give results for a tilt instability test case on very fine meshes.

Domaines: Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]

Hubert Baty, Florence Drui, Emmanuel Franck, Philippe Helluy, Christian Klingenberg, et al.. A kinetic method for solving the MHD equations. Application to the computation of tilt instability on uniform fine meshes. 2020. ⟨hal-02965967v1⟩