KINETIC-INDUCED MOMENT SYSTEMS FOR THE SAINT-VENANT EQUATIONS

(Received 20 December 2012; revised manuscript received 17 January 2013) Abstract: Based on the relation between kinetic Boltzmann-like transport equations and non- linear hyperbolic conservation laws, we derive kinetic-induced moment systems for the spatially one-dimensional shallow water equations (the Saint-Venant equations). Using Chapman-Enskog- like 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 clo- sure 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.