Affordable, entropy conserving and entropy stable flux functions for the ideal MHD equations

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• 作者：Andrew R. Winters ; ^{awinters@math.uni-koeln.de" class="auth_mail" title="E-mail the corresponding author} ; Gregor J. Gassner
• 关键词：Entropy conservation ; Entropy stable ; Ideal MHD equations ; Nonlinear hyperbolic conservation law ; Finite volume method
• 刊名：Journal of Computational Physics
• 出版年：2016
• 出版时间：1 January 2016
• 年：2016
• 卷：304
• 期：Complete
• 页码：72-108
• 全文大小：1799 K

文摘

In this work, we design an entropy stable, finite volume approximation for the ideal magnetohydrodynamics (MHD) equations. The method is novel as we design an affordable analytical expression of the numerical interface flux function that discretely preserves the entropy of the system. To guarantee the discrete conservation of entropy requires the addition of a particular source term to the ideal MHD system. Exact entropy conserving schemes cannot dissipate energy at shocks, thus to compute accurate solutions to problems that may develop shocks, we determine a dissipation term to guarantee entropy stability for the numerical scheme. Numerical tests are performed to demonstrate the theoretical findings of entropy conservation and robustness.