| Title: |
High order entropy stable schemes for the quasi-one-dimensional shallow water and compressible Euler equations |
| Authors: |
Chan, Jesse, Shukla, Khemraj, Wu, Xinhui, Liu, Ruofeng, Nalluri, Prani |
| Publication Year: |
2023 |
| Collection: |
Computer Science
Mathematics |
| Subject Terms: |
Mathematics - Numerical Analysis |
| More Details: |
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. |
| Document Type: |
Working Paper |
| Access URL: |
http://arxiv.org/abs/2307.12089 |
| Accession Number: |
edsarx.2307.12089 |
| Database: |
arXiv |
