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arXiv · 2201.05423

A skew-symmetric energy and entropy stable formulation of the compressible Euler equations

Jan Nordström
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Abstract

We show that a specific skew-symmetric form of nonlinear hyperbolic problems leads to energy and entropy bounds. Next, we exemplify by considering the compressible Euler equations in primitive variables, transform them to skew-symmetric form and show how to obtain energy and entropy estimates. Finally we show that the skew-symmetric formulation lead to energy and entropy stable discrete approximations if the scheme is formulated on summation-by-parts form.

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Jan Nordström. 2022-01-14. A skew-symmetric energy and entropy stable formulation of the compressible Euler equations. https://doi.org/10.1016/j.jcp.2022.111573

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