Analysis and Numerical Simulation of Hyperbolic Shallow Water Moment Equations (Communications in Computational Physics, 2020)
Shallow Water Moment Equations allow for vertical changes in the horizontal velocity, so that complex shallow flows can be described accurately. However, weshow that these models lack global hyperbolicity and the loss of hyperbolicity alreadyoccurs for small deviations from equilibrium. This leads to instabilities in a numericaltest case. We then derive new Hyperbolic Shallow Water Moment Equations based ona modification of the system matrix. The model can be written in analytical form andhyperbolicity can be proven for a large number of equations. A second variant of thismodel is obtained by generalizing the modification with the help of additional parameters. Numerical tests of a smooth periodic problem and a dam break problem usingthe new models yield accurate and fast solutions while guaranteeing hyperbolicity.
Keywords: Shallow water equation; moment method; hyperbolicity.