The Savage-Hutter theory: A system of partial differential equations for avalanche flows of snow, debris, and mudThis paper is based on the second author's general lecture at the GAMM meeting in March 2003 at Padova but it only treats a small portion of that talk and concentrates on dense granular flow down mountain sides, in particular the numerical treatment of the governing equations. The reason is that reviews of avalanching flows have previously appeared [8, 10] and our focus will be the presentation of numerical subtleties and the results implied by them.