Second-order schemes for conservation laws with discontinuous flux modelling clarifier-thickener units
type: Item
instance of: scholarly article
title: Second-order schemes for conservation laws with discontinuous flux modelling clarifier-thickener units
zbMATH Open document ID: 1204.65101
author: Héctor Torres
author: Raimund Bürger
author: Kenneth H. Karlsen
author: John D. Towers
published in: Numerische Mathematik
publication date: 2010-10-27T00:00:00Z
review text: The authors consider mainly a staggered first-order difference scheme and its second-order upgrading for a hyperbolic equation in one spatial variable modelling sediment suspension behaviour. The model contains a discontinuous flux, and in former works of the same authors [Comput. Vis. Sci. 6, No.~2--3, 83--91 (2004; Zbl 1299.76283)] the convergence of the first-order scheme to an entropy solution has been considered. Here they upgrade the scheme to (formal) second order by using corresponding correction terms and two kinds of limiters, a simple minmod and a new one (leading to a flux-total variation diminishing scheme), including here a correction for steady sonic rarefactions, too. For the nonlocal limiter proposed, an algorithm is formulated, its properties investigated and its numerical behaviour illustrated by a number of experiments and compared with the simpler scheme. Finally, an extended model including degenerate diffusion is considered also and solved by operator splitting (combining the former hyperbolic scheme and Crank-Nicolson), exhibiting good numerical results for the discontinuous solutions.
reviewed by: Gisbert Stoyan
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 65M12
zbMATH DE Number: 5806744
zbMATH Keywords: conservation law
zbMATH Keywords: discontinuous flux
zbMATH Keywords: first-order difference scheme
zbMATH Keywords: second-order correction
zbMATH Keywords: limiters
zbMATH Keywords: numerical experiments
zbMATH Keywords: sediment suspension
zbMATH Keywords: convergence
zbMATH Keywords: total variation diminishing scheme
zbMATH Keywords: algorithm
zbMATH Keywords: operator splitting
zbMATH Keywords: Crank-Nicolson
zbMATH Keywords: discontinuous solutions
MaRDI profile type: Publication
full work available at URL: s00211-010-0325-4
OpenAlex ID: W2031558692
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DOI: 10.1007/S00211-010-0325-4
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description: scientific article; zbMATH DE number 5806744