An accurate shock-capturing finite-difference method to solve the Savage-Hutter equations in avalanche dynamics

The Savage-Hutter equations of granular avalanche flows are a hyperbolic system of equations for the distribution of depth and depth-averaged velocity components tangential to the sliding bed. They involve two phenomenological parameters, the internal and the bed friction angles, which together define the earth pressure coefficient which assumes different values depending upon whether the flow is either diverging or contracting. Because of the hyperbolicity of the equations, since velocities may be supercritical, shock waves are often formed in avalanche flows. Numerical schemes solving these free surface flows must cope with smooth as well as non-smooth solutions. In this paper the Savage-Hutter equations in conservative form are solved with a shock-capturing technique, including a front-tracking method. This method can perform for parabolic similarity solutions for which the Lagrangian scheme is excellent, and it is even better in other situations when the latter fails.