Accurate Implementation of Rotating Magneto-Hydrodynamics in a Channel Geometry Using an Influence Matrix Method

Ringenbach, Jean-Clément; Tobias, Steven M.; Schneider, Tobias M.

doi:10.3390/math13162549

This is an early access version, the complete PDF, HTML, and XML versions will be available soon.

Open AccessArticle

Accurate Implementation of Rotating Magneto-Hydrodynamics in a Channel Geometry Using an Influence Matrix Method

by

Jean-Clément Ringenbach

^1,*

,

Steven M. Tobias

^2,*

and

Tobias M. Schneider

^1,*

¹

Emergent Complexity in Physical Systems, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland

²

School of Physics & Astronomy, University of Edinburgh, James Clerk Maxwell Building, Edinburgh EH9 3FD, UK

^*

Authors to whom correspondence should be addressed.

Mathematics 2025, 13(16), 2549; https://doi.org/10.3390/math13162549

Submission received: 31 March 2025 / Revised: 24 June 2025 / Accepted: 3 July 2025 / Published: 8 August 2025

(This article belongs to the Special Issue Numerical Simulation and Methods in Computational Fluid Dynamics)

Download Versions Notes

Abstract

We numerically study wall-bounded convectively driven magneto-hydrodynamic (MHD) flows subject to rotation in a Cartesian periodic channel. For the accurate treatment of the rotating MHD equations, we develop a pseudo-spectral simulation code with accurate treatment of boundary conditions for both velocity and magnetic fields. The solenoidal condition on the magnetic field is enforced by the addition of a fictitious magnetic pressure. This allows us to employ an influence matrix method with tau correction for the treatment of velocity and magnetic fields subject to Robin boundary conditions at the confining walls. We validate the developed method for the specific case of no slip velocity and perfectly conducting magnetic boundary conditions. The validation includes the accurate reproduction of linear stability thresholds and of turbulent statistics. The code shows favorable parallel scaling properties.

Keywords: MHD; influence matrix; DNS; dynamo; ChannelFlow

Share and Cite

MDPI and ACS Style

Ringenbach, J.-C.; Tobias, S.M.; Schneider, T.M. Accurate Implementation of Rotating Magneto-Hydrodynamics in a Channel Geometry Using an Influence Matrix Method. Mathematics 2025, 13, 2549. https://doi.org/10.3390/math13162549

AMA Style

Ringenbach J-C, Tobias SM, Schneider TM. Accurate Implementation of Rotating Magneto-Hydrodynamics in a Channel Geometry Using an Influence Matrix Method. Mathematics. 2025; 13(16):2549. https://doi.org/10.3390/math13162549

Chicago/Turabian Style

Ringenbach, Jean-Clément, Steven M. Tobias, and Tobias M. Schneider. 2025. "Accurate Implementation of Rotating Magneto-Hydrodynamics in a Channel Geometry Using an Influence Matrix Method" Mathematics 13, no. 16: 2549. https://doi.org/10.3390/math13162549

APA Style

Ringenbach, J.-C., Tobias, S. M., & Schneider, T. M. (2025). Accurate Implementation of Rotating Magneto-Hydrodynamics in a Channel Geometry Using an Influence Matrix Method. Mathematics, 13(16), 2549. https://doi.org/10.3390/math13162549

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

Article Menu

Accurate Implementation of Rotating Magneto-Hydrodynamics in a Channel Geometry Using an Influence Matrix Method

Abstract

Share and Cite

Article Metrics

Article Access Statistics

Further Information

Guidelines

MDPI Initiatives

Follow MDPI