A 5-wave relaxation solver for the shallow water MHD system

Abstract : The shallow water magnetohydrodynamic system describes the thin layer evolution of the solar tachocline. It is obtained from the three dimensional incompressible magnetohydrodynamic system similarly as the classical shallow water system is obtained from the incompressible Navier-Stokes equations. The system is hyperbolic and has two additional waves with respect to the shallow water system, the Alfven waves. These are linearly degenerate, and thus do not generate dissipation. In the present work we introduce a 5-wave approximate Riemann solver for the shallow water magnetohydrodynamic system, that has the property to be non dis-sipative on Alfven waves. It is obtained by solving a relaxation system of Suliciu type, and is similar to HLLC type solvers. The solver is positive and entropy satisfying, ensuring its robustness. It has sharp wave speeds, and does not involve any iterative procedure.
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https://hal-upec-upem.archives-ouvertes.fr/hal-01131293
Contributor : François Bouchut <>
Submitted on : Friday, March 13, 2015 - 11:56:33 AM
Last modification on : Wednesday, September 4, 2019 - 1:52:03 PM
Long-term archiving on : Monday, April 17, 2017 - 2:24:31 PM

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  • HAL Id : hal-01131293, version 1

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François Bouchut, Xavier Lhébrard. A 5-wave relaxation solver for the shallow water MHD system. 2015. ⟨hal-01131293v1⟩

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