  The Savage-Hutter (SH) equations are a hyperbolic system of nonlinear partial
differential equations describing the temporal evolution of the depth and depth
averaged velocity for modelling the avalanche of a shallow layer of granular
materials on an inclined surface. These equations admit the occurrence of shock
waves and vacuum fronts as in the shallow-water equations while possessing the
special reposing state of granular material. In this paper, we develop a
third-order Runge-Kutta discontinuous Galerkin (RKDG) method for the numerical
solution of the one-dimensional SH equations. We adopt a TVD slope limiter to
suppress numerical oscillations near discontinuities. And we give numerical
treatments for the avalanche front and for the bed friction to achieve the
well-balanced reposing property of granular materials. Numerical results of the
avalanche of cohesionless dry granular materials down an inclined and smoothly
transitioned to horizontal plane under various internal and bed friction angles
and slope angles are given to show the performance of the present numerical
scheme.
