An Offline-Online Riemann Solver for One-Dimensional Systems of Conservation Laws
In this paper, we present an exact Riemann solver for one-dimensional systems of conservation laws. The method is based on an offline-online computational decomposition. During the offline stage, we generate an accurate surrogate model for the solution to the Riemann problem for arbitrary left and r...
| Príomhchruthaitheoirí: | , , |
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| Formáid: | Alt |
| Teanga: | English |
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Springer Singapore
2016
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| Rochtain ar líne: | http://hdl.handle.net/1721.1/105761 https://orcid.org/0000-0002-3134-3730 |
| _version_ | 1826216587791695872 |
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| author | Taddei, Tommaso Quarteroni, Alfio Salsa, Sandro |
| author2 | Massachusetts Institute of Technology. Department of Mechanical Engineering |
| author_facet | Massachusetts Institute of Technology. Department of Mechanical Engineering Taddei, Tommaso Quarteroni, Alfio Salsa, Sandro |
| author_sort | Taddei, Tommaso |
| collection | MIT |
| description | In this paper, we present an exact Riemann solver for one-dimensional systems of conservation laws. The method is based on an offline-online computational decomposition. During the offline stage, we generate an accurate surrogate model for the solution to the Riemann problem for arbitrary left and right states. Then, during the online stage, we employ the surrogate model to generate accurate initial conditions for an iterative Newton solver. We present a mathematical analysis of the Riemann problem to justify the proposed approach. Finally, we illustrate its effectiveness by means of two numerical examples. |
| first_indexed | 2024-09-23T16:49:39Z |
| format | Article |
| id | mit-1721.1/105761 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T16:49:39Z |
| publishDate | 2016 |
| publisher | Springer Singapore |
| record_format | dspace |
| spelling | mit-1721.1/1057612022-09-29T21:49:46Z An Offline-Online Riemann Solver for One-Dimensional Systems of Conservation Laws Taddei, Tommaso Quarteroni, Alfio Salsa, Sandro Massachusetts Institute of Technology. Department of Mechanical Engineering Taddei, Tommaso In this paper, we present an exact Riemann solver for one-dimensional systems of conservation laws. The method is based on an offline-online computational decomposition. During the offline stage, we generate an accurate surrogate model for the solution to the Riemann problem for arbitrary left and right states. Then, during the online stage, we employ the surrogate model to generate accurate initial conditions for an iterative Newton solver. We present a mathematical analysis of the Riemann problem to justify the proposed approach. Finally, we illustrate its effectiveness by means of two numerical examples. 2016-12-08T21:50:18Z 2017-04-11T21:29:34Z 2016-06 2015-01 2016-11-15T04:40:29Z Article http://purl.org/eprint/type/JournalArticle 2305-221X 2305-2228 http://hdl.handle.net/1721.1/105761 Taddei, Tommaso, Alfio Quarteroni, and Sandro Salsa. “An Offline-Online Riemann Solver for One-Dimensional Systems of Conservation Laws.” Vietnam Journal of Mathematics 44, no. 4 (June 11, 2016): 873–891. https://orcid.org/0000-0002-3134-3730 en http://dx.doi.org/10.1007/s10013-016-0212-0 Vietnam Journal of Mathematics Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. Vietnam Academy of Science and Technology (VAST) and Springer Science+Business Media Singapore application/pdf Springer Singapore Springer Singapore |
| spellingShingle | Taddei, Tommaso Quarteroni, Alfio Salsa, Sandro An Offline-Online Riemann Solver for One-Dimensional Systems of Conservation Laws |
| title | An Offline-Online Riemann Solver for One-Dimensional Systems of Conservation Laws |
| title_full | An Offline-Online Riemann Solver for One-Dimensional Systems of Conservation Laws |
| title_fullStr | An Offline-Online Riemann Solver for One-Dimensional Systems of Conservation Laws |
| title_full_unstemmed | An Offline-Online Riemann Solver for One-Dimensional Systems of Conservation Laws |
| title_short | An Offline-Online Riemann Solver for One-Dimensional Systems of Conservation Laws |
| title_sort | offline online riemann solver for one dimensional systems of conservation laws |
| url | http://hdl.handle.net/1721.1/105761 https://orcid.org/0000-0002-3134-3730 |
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