Volume 20, Issue 4
Godunov-Type Numerical Methods for a Model of Granular Flow on Open Tables with Walls

Adimurthi, Aekta Aggarwal & G. D. Veerappa Gowda

Commun. Comput. Phys., 20 (2016), pp. 1071-1105.

Published online: 2018-04

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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.

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@Article{CiCP-20-1071, author = {Adimurthi, Aekta Aggarwal and G. D. Veerappa Gowda}, title = {Godunov-Type Numerical Methods for a Model of Granular Flow on Open Tables with Walls}, journal = {Communications in Computational Physics}, year = {2018}, volume = {20}, number = {4}, pages = {1071--1105}, 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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.290615.060516a}, url = {http://global-sci.org/intro/article_detail/cicp/11183.html} }
TY - JOUR T1 - Godunov-Type Numerical Methods for a Model of Granular Flow on Open Tables with Walls AU - Adimurthi, Aekta Aggarwal & G. D. Veerappa Gowda JO - Communications in Computational Physics VL - 4 SP - 1071 EP - 1105 PY - 2018 DA - 2018/04 SN - 20 DO - http://dor.org/10.4208/cicp.290615.060516a UR - https://global-sci.org/intro/cicp/11183.html KW - AB -

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.

Adimurthi, Aekta Aggarwal & G. D. Veerappa Gowda. (1970). Godunov-Type Numerical Methods for a Model of Granular Flow on Open Tables with Walls. Communications in Computational Physics. 20 (4). 1071-1105. doi:10.4208/cicp.290615.060516a
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