Geodesic
Divergence-free MHD Simulations with the HERACLES Code
J. Vides1 ; E. Audit2 ; H. Guillard3 ; B. Nkonga3
1 Inria, Maison de la Simulation, USR 3441, Gif-sur-Yvette, France.
2 CEA, Maison de la Simulation, USR 3441, Gif-sur-Yvette, France.
3 Université de Nice-Sophia Antipolis, UMR CNRS 7351 & Inria Sophia Antipolis, France.
ESAIM. Proceedings, Tome 43 (2013), pp. 180-194.

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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.
DOI : 10.1051/proc/201343012

J. Vides 1 ; E. Audit 2 ; H. Guillard 3 ; B. Nkonga 3

1 Inria, Maison de la Simulation, USR 3441, Gif-sur-Yvette, France.
2 CEA, Maison de la Simulation, USR 3441, Gif-sur-Yvette, France.
3 Université de Nice-Sophia Antipolis, UMR CNRS 7351 & Inria Sophia Antipolis, France. 
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     author = {J. Vides and E. Audit and H. Guillard and B. Nkonga},
     title = {Divergence-free {MHD} {Simulations} with the {HERACLES} {Code}},
     journal = {ESAIM. Proceedings},
     pages = {180--194},
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     doi = {10.1051/proc/201343012},
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J. Vides; E. Audit; H. Guillard; B. Nkonga. Divergence-free MHD Simulations with the HERACLES Code. ESAIM. Proceedings, Tome 43 (2013), pp. 180-194. doi : 10.1051/proc/201343012. http://geodesic.mathdoc.fr/articles/10.1051/proc/201343012/

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