Advanced lattice Boltzmann scheme for high-Reynolds-number magneto-hydrodynamic flows

ABSTRACT

Is the lattice Boltzmann method suitable to investigate numerically high-Reynolds-number magneto-hydrodynamic (MHD) flows? It is shown that a standard approach based on the Bhatnagar–Gross–Krook (BGK) collision operator rapidly yields unstable simulations as the Reynolds number increases. In order to circumvent this limitation, it is here suggested to address the collision procedure in the space of central moments for the fluid dynamics. Therefore, an hybrid lattice Boltzmann scheme is introduced, which couples a central-moment scheme for the velocity with a BGK scheme for the space-and-time evolution of the magnetic field. This method outperforms the standard approach in terms of stability, allowing us to simulate high-Reynolds-number MHD flows with non-unitary Prandtl number while maintaining accuracy and physical consistency.

KEYWORDS:

• Lattice Boltzmann method
• magnetohydrodynamics
• turbulence

Note

In the Supplementary Material, a script CentralMoments_MHD.m is attached allowing the reader to derive the entire formulation.

Acknowledgements

This work has been carried out within the framework of the ‘Programme Avenir Lyon Saint-Etienne’ at the Université de Lyon (ANR-11-IDEX-0007) under the Program ‘Investissements d’Avenir’ operated by the French National Research Agency. The research leading to these results has received funding from the People Programme (Marie Curie Actions) of the European Union's Seventh Framework Programme (FP7/2007-2013) under REA grant agreement no PCOFUND-GA-2013-609102, through the PRESTIGE programme coordinated by Campus France. This article is based upon work from COST Action MP1305, supported by COST (European Cooperation in Science and Technology). The authors are grateful to W.J.T. Bos and N. Plihon for useful hints about magneto-hydrodynamic turbulence.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Programme Avenir Lyon Saint-Etienne [grant number ANR-11-IDEX-0007]; People Programme (Marie Curie Actions) of the European Union's Seventh Framework Programme [grant number FP7/2007-2013]; REA [grant number PCOFUND-GA-2013-609102].