Hyperbolic conservation laws with space-dependent fluxes: II. General study of numerical fluxes
type: Item
instance of: scholarly article
title: Hyperbolic conservation laws with space-dependent fluxes: II. General study of numerical fluxes
zbMATH Open document ID: 1068.65109
author: Peng Zhang
author: Ruxun Liu
published in: Journal of Computational and Applied Mathematics
publication date: 2005-02-23T00:00:00Z
review text: [For part I see ibid. 156, No.~1, 1--21 (2003; Zbl 1031.35104).] The authors consider the initial value problem of the following scalar conservation equation \[ \begin{cases} u_t+f(u(x,t),a(x))_x=0,\quad & x\in\mathbb{R}=(-\infty,+\infty),\;t\geq 0\\ u(x,0)=u_0(x),\end{cases}\tag{1} \] where \(a(x)\) is the known function and \(u(x,t)\) is the unknown function. Some generalized fluxes of the Godunov and Engquist-Osher types are verified to enjoy more theoretical properties without the restrictions of the previous works. Moreover, the authors show that the resulting numerical solutions are characterized by an \(L^\infty\) contraction. Numerical examples of the authors show the convergence to exact solutions and very good resolution of discontinuities. The numerical results are compared to some ``simple'' generalization of the Godunov, the Engquist-Osher, and the local Lax-Friedrichs fluxes.
reviewed by: Messoud Efendiev
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 35L65
Mathematics Subject Classification ID: 65M12
zbMATH DE Number: 2137366
zbMATH Keywords: confinedness
zbMATH Keywords: consistency
zbMATH Keywords: monotonicity
zbMATH Keywords: nonstrictly hyperbolic equation
zbMATH Keywords: comparison of methods
zbMATH Keywords: Godunov method
zbMATH Keywords: Engquist-Osher method
zbMATH Keywords: numerical examples
zbMATH Keywords: convergence
zbMATH Keywords: resolution of discontinuities
zbMATH Keywords: local Lax-Friedrichs fluxes
describes a project that uses: HLLE
MaRDI profile type: Publication
full work available at URL: j.cam.2004.07.005
OpenAlex ID: W1972230643
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DOI: 10.1016/J.CAM.2004.07.005
description: scientific article; zbMATH DE number 2137366