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1 TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

1 2013

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Kinetic-induced moment systems for the Saint-Venant equations

Gil Montoya D. C., Struckmeier J.

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

2013

Vol.17, No 1-2

63--90

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-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 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.