Gas Kinetic Scheme for Anisotropic Savage-Hutter Model (Communications in Computational Physics, 2013)
The gas-kinetic scheme is applied to a depth-integrated continuum modelfor avalanche flows, namely the Savage-Hutter model. In this method, the continuumfluxes are calculated based on the pseudo particle motions which are relaxed from nonequilibrium to equilibrium states. The processes are described by the Bhatnagar-Gross-Krook (BGK) equation. The benefit of this scheme is its capability to resolve shockdiscontinuities sharply and to handle the vacuum state without special treatments.Because the Savage-Hutter equation bears an anisotropic stress on the tangential spaceof the topography, the equilibrium distribution function of the microscopic particlesare shown to be bi-Maxwellian. These anisotropic stresses are the key to preserve thecoordinate objectivity in the Savage-Hutter model. The effect of the anisotropic stressis illustrated by two examples: an axisymmetric dam break and a finite mass sliding onan inclined plane chute. It is found that the propagation of the flow fronts significantlydepends on the orientation of the principal axes of the tangential stresses.