High order entropy stable schemes for the quasi-one-dimensional shallow water and compressible Euler equations
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866914637126041600 |
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| author | Chan, Jesse Shukla, Khemraj Wu, Xinhui Liu, Ruofeng Nalluri, Prani |
| author_facet | Chan, Jesse Shukla, Khemraj Wu, Xinhui Liu, Ruofeng Nalluri, Prani |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_12089 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | High order entropy stable schemes for the quasi-one-dimensional shallow water and compressible Euler equations Chan, Jesse Shukla, Khemraj Wu, Xinhui Liu, Ruofeng Nalluri, Prani Numerical Analysis 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. |
| title | High order entropy stable schemes for the quasi-one-dimensional shallow water and compressible Euler equations |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2307.12089 |