Regularization of the Shock Wave Solution to the Riemann Problem for the Relativistic Burgers Equation

Regularization of the Shock Wave Solution to the Riemann Problem for the Relativistic Burgers Equation

The regularization of the shock wave solution to the Riemann problem for the relativistic Burgers equation is considered. For Riemann initial data consisting of a single decreasing jump, we find that the regularization of nonlinear convective term cannot capture the correct shock wave solution. In o...

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Main Authors: Ting Zhang, Chun Shen
Format: Article
Language:English
Published: Hindawi Limited 2014-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2014/178672
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spelling doaj-e87df0f5e6764cb59299b86bbb5c64d72020-11-25T01:48:27ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/178672178672Regularization of the Shock Wave Solution to the Riemann Problem for the Relativistic Burgers EquationTing Zhang0Chun Shen1School of Mathematics and Statistics Science, Ludong University, Yantai, Shandong 264025, ChinaSchool of Mathematics and Statistics Science, Ludong University, Yantai, Shandong 264025, ChinaThe regularization of the shock wave solution to the Riemann problem for the relativistic Burgers equation is considered. For Riemann initial data consisting of a single decreasing jump, we find that the regularization of nonlinear convective term cannot capture the correct shock wave solution. In order to overcome it, we consider a new regularization technique called the observable divergence method introduced by Mohseni and discover that it can capture the correct shock wave solution. In addition, we take the Helmholtz filter for the fully explicit computation.http://dx.doi.org/10.1155/2014/178672
collection DOAJ
language English
format Article
sources DOAJ
author Ting Zhang
Chun Shen
spellingShingle Ting Zhang
Chun Shen
Regularization of the Shock Wave Solution to the Riemann Problem for the Relativistic Burgers Equation
Abstract and Applied Analysis
author_facet Ting Zhang
Chun Shen
author_sort Ting Zhang
title Regularization of the Shock Wave Solution to the Riemann Problem for the Relativistic Burgers Equation
title_short Regularization of the Shock Wave Solution to the Riemann Problem for the Relativistic Burgers Equation
title_full Regularization of the Shock Wave Solution to the Riemann Problem for the Relativistic Burgers Equation
title_fullStr Regularization of the Shock Wave Solution to the Riemann Problem for the Relativistic Burgers Equation
title_full_unstemmed Regularization of the Shock Wave Solution to the Riemann Problem for the Relativistic Burgers Equation
title_sort regularization of the shock wave solution to the riemann problem for the relativistic burgers equation
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2014-01-01
description The regularization of the shock wave solution to the Riemann problem for the relativistic Burgers equation is considered. For Riemann initial data consisting of a single decreasing jump, we find that the regularization of nonlinear convective term cannot capture the correct shock wave solution. In order to overcome it, we consider a new regularization technique called the observable divergence method introduced by Mohseni and discover that it can capture the correct shock wave solution. In addition, we take the Helmholtz filter for the fully explicit computation.
url http://dx.doi.org/10.1155/2014/178672
work_keys_str_mv AT tingzhang regularizationoftheshockwavesolutiontotheriemannproblemfortherelativisticburgersequation
AT chunshen regularizationoftheshockwavesolutiontotheriemannproblemfortherelativisticburgersequation
_version_ 1725012160465076224

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