KINETIC-INDUCED MOMENT SYSTEMS FOR THE SAINT-VENANT EQUATIONS

Abstract

Based on the relation between kinetic Boltzmann-like transport equations and nonlinear hyperbolic conservation laws, we derive kinetic-induced moment systems for the spatially one-dimensional shallow water equations (the Saint-Venant equations). Using Chapman-Enskoglike asymptotic expansion techniques in terms of the relaxation parameter of the kinetic equation, the resulting moment systems are asymptotically closed without the need for an additional closure relation. Moreover, the new second order moment equation for the (asymptotically) third order system may act as a monitoring function to detect shock and rarefaction waves, which we confirm by a number of numerical experiments.

Keywords

• Saint-Venant equations
• shallow water equations
• Boltzmann equation
• hyperbolic conservation laws
• kinetic models and representations
• relaxation systems