Year: 2020
Author: Julian Koellermeier, Marvin Rominger
Communications in Computational Physics, Vol. 28 (2020), Iss. 3 : pp. 1038–1084
Abstract
Shallow Water Moment Equations allow for vertical changes in the horizontal velocity, so that complex shallow flows can be described accurately. However, we show that these models lack global hyperbolicity and the loss of hyperbolicity already occurs for small deviations from equilibrium. This leads to instabilities in a numerical test case. We then derive new Hyperbolic Shallow Water Moment Equations based on a modification of the system matrix. The model can be written in analytical form and hyperbolicity can be proven for a large number of equations. A second variant of this model is obtained by generalizing the modification with the help of additional parameters. Numerical tests of a smooth periodic problem and a dam break problem using the new models yield accurate and fast solutions while guaranteeing hyperbolicity.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2019-0065
Communications in Computational Physics, Vol. 28 (2020), Iss. 3 : pp. 1038–1084
Published online: 2020-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 47
Keywords: Shallow water equation moment method hyperbolicity.