Shock capturing and front tracking methods for granular avalanches

Tai, Y.-C. and Noelle, S. and Gray, J.M.N.T. (2002) Shock capturing and front tracking methods for granular avalanches. Journal of Computational Physics, 175. pp. 269-301. ISSN 0021-9991

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Abstract

Shock formations are observed in granular avalanches when supercritical flow merges into a region of subcritical flow. In this paper we employ a shock-capturing numerical scheme for the one-dimensional Savage–Hutter theory of granular flow to describe this phenomenon. A Lagrangian moving mesh scheme applied to the nonconservative form of the equations reproduces smooth solutions of these free boundary problems very well, but fails when shocks are formed. A nonoscillatory central (NOC) difference scheme with TVD limiter or WENO cell reconstruction for the conservative equations is therefore introduced. For the avalanche free boundary problems it must be combined with a front-tracking method, developed here, to properly describe the margin evolution. It is found that this NOC scheme combined with the front-tracking module reproduces both the shock wave and the smooth solution accurately. A piecewise quadratic WENO reconstruction improves the smoothness of the solution near local extrema. The schemes are checked against exact solutions for (1) an upward moving shock wave, (2) the motion of a parabolic cap down an inclined plane, and (3) the motion of a parabolic cap down a curved slope ending in a flat run-out region, where a shock is formed as the avalanche comes to a halt.

Item Type: Article
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 35 Partial differential equations
MSC 2010, the AMS's Mathematics Subject Classification > 70 Mechanics of particles and systems
MSC 2010, the AMS's Mathematics Subject Classification > 74 Mechanics of deformable solids
MSC 2010, the AMS's Mathematics Subject Classification > 76 Fluid mechanics
Depositing User: Prof JMNT Gray
Date Deposited: 17 Nov 2006
Last Modified: 20 Oct 2017 14:12
URI: http://eprints.maths.manchester.ac.uk/id/eprint/648

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