Analysis and Numerical Simulation of Hyperbolic Shallow Water Moment Equations

Julian Koellermeier*, Marvin Rominger

*Bijbehorende auteur voor dit werk

OnderzoeksoutputAcademicpeer review

10 Citaten (Scopus)


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.
Originele taal-2English
Pagina's (van-tot)1038-1084
Aantal pagina's46
TijdschriftCommunications in Computational Physics
StatusPublished - jul.-2020
Extern gepubliceerdJa

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