Cone-grid scheme for solving hyperbolic systems of conservation laws and one application
type: Item
instance of: scholarly article
title: Cone-grid scheme for solving hyperbolic systems of conservation laws and one application
zbMATH Open document ID: 1435.65151
author: Mahmoud A. E. Abdelrahman
published in: Computational and Applied Mathematics
publication date: 2018-11-05T00:00:00Z
review text: This paper deals with the numerical simulation of the solution of the so-called phonon-Bose system in one-space dimension applying a numerical method obtained using the cone-grid approach. This approach was introduced in the author's work with [\textit{M. Kunik}, J. Comput. Phys. 275, 213--235 (2014; Zbl 1349.76579)] and the first part of the paper (Section 2) differs in minor details of the mentioned paper. The numerical method intoduced here is defined particularizing the first part to the particular system under consideration (Section 3). Numerical results illustrating the behaviour of the numerical solution in different scenarios are also included (Section 4).
Mathematics Subject Classification ID: 65M25
Mathematics Subject Classification ID: 35L45
Mathematics Subject Classification ID: 35L60
Mathematics Subject Classification ID: 35L65
Mathematics Subject Classification ID: 35L67
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 76L05
zbMATH DE Number: 6973274
zbMATH Keywords: hyperbolic conservation laws
zbMATH Keywords: cone-grid scheme
zbMATH Keywords: heat-conduction model
zbMATH Keywords: rarefaction waves (fans)
zbMATH Keywords: shock waves
zbMATH Keywords: initial value problems
zbMATH Keywords: \(L^1\)-stability
reviewed by: J. A. Ferreira
MaRDI profile type: Publication
full work available at URL: s40314-017-0527-9
OpenAlex ID: W2765865313
cites work: A new front tracking scheme for the ultra-relativistic Euler equations
cites work: Entropy and causality as criteria for the existence of shock waves in low temperature heat conduction
cites work: Q4503985
cites work: Initial and boundary value problems of hyperbolic heat conduction
cites work: Kinetic flux-vector splitting schemes for the hyperbolic heat conduction
DOI: 10.1007/S40314-017-0527-9
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description: scientific article; zbMATH DE number 6973274