Ideal GLM-MHD: About the entropy consistent nine-wave magnetic field divergence diminishing ideal magnetohydrodynamics equations

JOURNAL OF COMPUTATIONAL PHYSICS

卷:364

Article

Derigs, Dominik¹  Winters, Andrew R.²  Gassner, Gregor J.²  Walch, Stefanie¹  Bohm, Marvin² 

[1] Univ Cologne, Phys Inst 1, Zulpicher Str 77, D-50937 Cologne, Germany

[2] Univ Cologne, Math Inst, Weyertal 86-90, D-50931 Cologne, Germany

关键词: Magnetohydrodynamics;    Entropy stability;    Divergence-free magnetic field;    Divergence cleaning;   

DOI  :  10.1016/j.jcp.2018.03.002

来源: Elsevier

【 摘 要 】

The paper presents two contributions in the context of the numerical simulation of magnetized fluid dynamics. First, we show how to extend the ideal magnetohydrodynamics (MHD) equations with an inbuilt magnetic field divergence cleaning mechanism in such a way that the resulting model is consistent with the second law of thermodynamics. As a byproduct of these derivations, we show that not all of the commonly used divergence cleaning extensions of the ideal MHD equations are thermodynamically consistent. Secondly, we present a numerical scheme obtained by constructing a specific finite volume discretization that is consistent with the discrete thermodynamic entropy. It includes a mechanism to control the discrete divergence error of the magnetic field by construction and is Galilean invariant. We implement the new high-order MHD solver in the adaptive mesh refinement code FLASH where we compare the divergence cleaning efficiency to the constrained transport solver available in FLASH (unsplit staggered mesh scheme). (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free