期刊
JOURNAL OF COMPUTATIONAL PHYSICS
卷 364, 期 -, 页码 420-467出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2018.03.002
关键词
Magnetohydrodynamics; Entropy stability; Divergence-free magnetic field; Divergence cleaning
资金
- Bonn-Cologne Graduate School for Physics and Astronomy (BCGS) through the Excellence Initiative [GSC 260]
- Deutsche Forschungsgemeinschaft (DFG) [SPP 1573]
- European Research Council (RADFEEDBACK) [679852]
- European Research Council [71448]
- Gauss Centre for Supercomputing e.V.
- [Sonderforschungsbereich (SFB) 956]
- European Research Council (ERC) [679852] Funding Source: European Research Council (ERC)
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.
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