Gas Kinetic Scheme for Anisotropic Savage-Hutter Model

The gas-kinetic scheme is applied to a depth-integrated continuum model for avalanche flows,namely the Savage-Hutter model.In this method,the continuum fluxes are calculated based on the pseudo particle motions which are relaxed from nonequilibrium to equilibrium states.The processes are described by the Bhatnagar-GrossKrook(BGK)equation.The benefit of this scheme is its capability to resolve shock discontinuities sharply and to handle the vacuum state without special treatments.Because the Savage-Hutter equation bears an anisotropic stress on the tangential space of the topography,the equilibrium distribution function of the microscopic particles are shown to be bi-Maxwellian.These anisotropic stresses are the key to preserve the coordinate objectivity in the Savage-Hutter model.The effect of the anisotropic stress is illustrated by two examples:an axisymmetric dam break and a finite mass sliding on an inclined plane chute.It is found that the propagation of the flow fronts significantly depends on the orientation of the principal axes of the tangential stresses.