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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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/178672 |
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| _version_ | 1832550664578793472 |
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| author | Ting Zhang Chun Shen |
| author_facet | Ting Zhang Chun Shen |
| author_sort | Ting Zhang |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-e87df0f5e6764cb59299b86bbb5c64d7 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-e87df0f5e6764cb59299b86bbb5c64d72025-02-03T06:06:18ZengWileyAbstract 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 |
| spellingShingle | Ting Zhang Chun Shen Regularization of the Shock Wave Solution to the Riemann Problem for the Relativistic Burgers Equation Abstract and Applied Analysis |
| title | 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_short | 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 |
| url | http://dx.doi.org/10.1155/2014/178672 |
| work_keys_str_mv | AT tingzhang regularizationoftheshockwavesolutiontotheriemannproblemfortherelativisticburgersequation AT chunshen regularizationoftheshockwavesolutiontotheriemannproblemfortherelativisticburgersequation |