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Analysis and Numerical Simulation of Hyperbolic Shallow Water Moment Equations

Analysis and Numerical Simulation of Hyperbolic Shallow Water Moment Equations
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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.

Author Details

Julian Koellermeier

Marvin Rominger

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