Hybrid entropy stable HLL-type Riemann solvers for hyperbolic conservation laws

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• 作者：Birte Schmidtmann^a ; ^{schmidtmann@mathcces.rwth-aachen.de} ; Andrew R. Winters^b
• 关键词：Entropy stability ; Ideal magnetohydrodynamics ; HLL ; Riemann solver ; Discrete entropy inequality
• 刊名：Journal of Computational Physics
• 出版年：2017
• 出版时间：1 February 2017
• 年：2017
• 卷：330
• 期：Complete
• 页码：566-570
• 全文大小：286 K
• 卷排序：330

文摘

It is known that HLL-type schemes are more dissipative than schemes based on characteristic decompositions. However, HLL-type methods offer greater flexibility to large systems of hyperbolic conservation laws because the eigenstructure of the flux Jacobian is not needed. We demonstrate in the present work that several HLL-type Riemann solvers are provably entropy stable. Further, we provide convex combinations of standard dissipation terms to create hybrid HLL-type methods that have less dissipation while retaining entropy stability. The decrease in dissipation is demonstrated for the ideal MHD equations with a numerical example.