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

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Abstract:

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.

Document Type: Research Article

DOI: http://dx.doi.org/10.3189/172756401781819733

Publication date: January 1, 2001

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  • The Annals of Glaciology is a peer-reviewed, thematic journal published 2 to 4 times a year by the International Glaciological Society (IGS). Publication frequency is determined and volume/issue numbers assigned by the IGS Council on a year-to-year basis and with a lead time of 3 to 4 years. The Annals of Glaciology is included in the ISI Science Citation Index from volume 50, number 50 onwards.

    Themes can be on any aspect of the study of snow and ice. Individual members can make a suggestion for a theme for an Annals issue to the Secretary General, who will forward it to the IGS Publications Committee. The IGS Publication Committee will make a recommendation for an individual themed Annals issue, together with a potential Annals Chief Editor for that issue, to IGS Council. The IGS Council will make the decision whether to proceed, taking into account the spread of topics and the overall capacity for publication of pages in Annals.

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