Micro-Macro Simulation of Shallow Water Moment Equations

Abstract: Shallow flows are governed by the Navier-Stokes equations. They are commonly modelled using the shallow water equations, a great simplification of the Navier-Stokes equations, which often yields inaccurate results. For that reason, a model called shallow water moment equations has been developed. It uses more equations and variables than the shallow water equations. While this model is significantly more accurate, it is also computationally more expensive. To speed up computations, the micro-macro method may be used. The micro-macro method switches between two models of varying levels of detail allowing for larger stable time steps. In this paper we formulate the micro-macro method for shallow water moment equations. We perform a theoretical runtime analysis of the method and present a series of results for a dam break test and a wave transport test. The micro-macro method achieves a significant speed-up while retaining a sufficient level of accuracy.