Symbolic computation of the flow of granular avalanches

✍ Scribed by Stuart B. Savage

• Publisher: Elsevier Science
• Year: 1990
• Tongue: English
• Weight: 830 KB
• Volume: 9
• Category: Article
• ISSN: 0747-7171
• DOI: 10.1016/s0747-7171(08)80025-9

✦ Synopsis

The two-dimenslonal flow of a mass of cohesionless granular materiaI down a rough bed is studied by the use of the method of strMned coordinates. The work is relevant to the motion of rockfalls, ice avalanches and dense flowing snow avalanches. By appropriate non-dimensionalization, a small parameter e, which is the ratio of the characteristic length to depth of the pile, appears in the equations of motion. Perturbation expansions for the depth and velocity profiles of the moving mass, and the strained coordinate are introduced. The differentia/equations for terms of various orders are solved and the resulting divergent series are summed by the use of Shanks transformations and Pad~ approximaats. The analysis is carried out with the symbolic manipulation package I%EDUCE 3.3 and these results are translated by means of GENTI~AiN into C-code for numerical evaluation. The analytical form of the solution suggested the existence of similarity solutions for certain initial conditions. The analysis also demonstrated the inadequacies of a finite difference routine; this ted to the development of a much improved numerica/scheme.