@Article{CiCP-28-1038,
author = {Koellermeier , Julian and Rominger , Marvin},
title = {Analysis and Numerical Simulation of Hyperbolic Shallow Water Moment Equations},
journal = {Communications in Computational Physics},
year = {2020},
volume = {28},
number = {3},
pages = {1038--1084},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2019-0065},
url = {http://global-sci.org/intro/article_detail/cicp/17675.html}
}