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arXiv · 2307.12089

High order entropy stable schemes for the quasi-one-dimensional shallow water and compressible Euler equations

Jesse Chan·Khemraj Shukla·Xinhui Wu·Ruofeng Liu·Prani Nalluri
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Abstract

High order schemes are known to be unstable in the presence of shock discontinuities or under-resolved solution features for nonlinear conservation laws. Entropy stable schemes address this instability by ensuring that physically relevant solutions satisfy a semi-discrete entropy inequality independently of discretization parameters. This work extends high order entropy stable schemes to the quasi-1D shallow water equations and the quasi-1D compressible Euler equations, which model one-dimensional flows through channels or nozzles with varying width. We introduce new non-symmetric entropy conservative finite volume fluxes for both sets of quasi-1D equations, as well as a generalization of the entropy conservation condition to non-symmetric fluxes. When combined with an entropy stable interface flux, the resulting schemes are high order accurate, conservative, and semi-discretely entropy stable. For the quasi-1D shallow water equations, the resulting schemes are also well-balanced.

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Jesse Chan, Khemraj Shukla, Xinhui Wu, Ruofeng Liu, Prani Nalluri. 2023-07-22. High order entropy stable schemes for the quasi-one-dimensional shallow water and compressible Euler equations. https://arxiv.org/abs/2307.12089

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