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

This paper is devoted to the simulation of Magnetohydrohynamics (MHD) flows with complex structures. This kind of flow present instabilities that generate shock waves. We propose a robust and accurate numerical method based on the Lattice Boltzmann methodology. We 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. This 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). We also give results for a tilt instability test case on very fine meshes.