@Article{CiCP-20-4,
author = {},
title = {Godunov-Type Numerical Methods for a Model of Granular Flow on Open Tables with Walls},
journal = {Communications in Computational Physics},
year = {2016},
volume = {20},
number = {4},
pages = {1071--1105},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.290615.060516a},
url = {https://global-sci.com/article/80228/godunov-type-numerical-methods-for-a-model-of-granular-flow-on-open-tables-with-walls}
}