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Godunov-Type Numerical Methods for a Model of Granular Flow on Open Tables with Walls

Published online by Cambridge University Press:  05 October 2016

Adimurthi
Affiliation:
TIFR Centre for Applicable Mathematics, Bangalore 560065, India
Aekta Aggarwal
Affiliation:
The Indian Institute of Management Indore, Prabandh Shikhar, Rau Pithampur Road, Indore, Madhya Pradesh 453556, India
G. D. Veerappa Gowda
Affiliation:
TIFR Centre for Applicable Mathematics, Bangalore 560065, India
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Abstract

We propose and analyse finite volume Godunov type methods based on discontinuous flux for a 2×2 system of non-linear partial differential equations proposed by Hadeler and Kuttler to model the dynamics of growing sandpiles generated by a vertical source on a flat bounded rectangular table. The problem considered here is the so-called partially open table problem where sand is blocked by a wall (of infinite height) on some part of the boundary of the table. The novelty here is the corresponding modification of boundary conditions for the standing and the rolling layers and generalization of the techniques of the well-balancedness proposed in [1]. Presence of walls may lead to unbounded or discontinuous surface flow density at equilibrium resulting in solutions with singularities propagating from the extreme points of the walls. A scheme has been proposed to approximate efficiently the Hamiltonians with the coefficients which can be unbounded and discontinuous. Numerical experiments are presented to illustrate that the proposed schemes detect these singularities in the equilibrium solutions efficiently and comparisons are made with the previously studied finite difference and Semi-Lagrangian approaches by Finzi Vita et al.

Type
Research Article
Copyright
Copyright © Global-Science Press 2016 

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References

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