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Divergence-Free MHD Simulations with the HERACLES Code

Jeaniffer Vides 1, 2 Edouard Audit 1 Hervé Guillard 2, 3 Boniface Nkonga 2, 3 
2 CASTOR - Control, Analysis and Simulations for TOkamak Research
CRISAM - Inria Sophia Antipolis - Méditerranée , JAD - Laboratoire Jean Alexandre Dieudonné
Abstract : Numerical simulations of the magnetohydrodynamics (MHD) equations have played a significant role in plasma research over the years. The need of obtaining physical and stable solutions to these equations has led to the development of several schemes, all requiring to satisfy and preserve the divergence constraint of the magnetic field numerically. In this paper, we aim to show the importance of maintaining this constraint numerically. We investigate in particular the hyperbolic divergence cleaning technique applied to the ideal MHD equations on a collocated grid and compare it to the constrained transport technique that uses a staggered grid to maintain the property. The methods are implemented in the software HERACLES and several numerical tests are presented, where the robustness and accuracy of the different schemes can be directly compared.
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Submitted on : Friday, September 5, 2014 - 2:48:40 PM
Last modification on : Thursday, August 4, 2022 - 4:58:36 PM

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Jeaniffer Vides, Edouard Audit, Hervé Guillard, Boniface Nkonga. Divergence-Free MHD Simulations with the HERACLES Code. ESAIM: Proc., Dec 2013, Marseille, France. pp.180-194, ⟨10.1051/proc/201343012⟩. ⟨hal-01061303⟩



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