Study of a Model Equation in Detonation Theory: Multidimensional Effects
We extend the reactive Burgers equation presented in [A. R. Kasimov, L. M. Faria, and R. R. Rosales, Phys. Rev. Lett., 110 (2013), 104104], [L. M. Faria, A. R. Kasimov, and R. R. Rosales, SIAM J. Appl. Math., 74 (2014), pp. 547--570] to include multidimensional effects. Furthermore, we explain how t...
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| Format: | Article |
| Language: | en_US |
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Society for Industrial and Applied Mathematics (SIAM)
2016
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| Online Access: | http://hdl.handle.net/1721.1/103580 https://orcid.org/0000-0002-8828-5930 https://orcid.org/0000-0002-8129-2548 |
| _version_ | 1826208474319552512 |
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| author | Faria, Luiz Kasimov, A. R. Rosales, Rodolfo |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Faria, Luiz Kasimov, A. R. Rosales, Rodolfo |
| author_sort | Faria, Luiz |
| collection | MIT |
| description | We extend the reactive Burgers equation presented in [A. R. Kasimov, L. M. Faria, and R. R. Rosales, Phys. Rev. Lett., 110 (2013), 104104], [L. M. Faria, A. R. Kasimov, and R. R. Rosales, SIAM J. Appl. Math., 74 (2014), pp. 547--570] to include multidimensional effects. Furthermore, we explain how the model can be rationally justified following the ideas of the asymptotic theory developed in [L. M. Faria, A. R. Kasimov, and R. R. Rosales, J. Fluid Mech., 784 (2015), pp. 163--198]. The proposed model is a forced version of the unsteady small disturbance transonic flow equations. We show that for physically reasonable choices of forcing functions, traveling wave solutions akin to detonation waves exist. It is demonstrated that multidimensional effects play an important role in the stability and dynamics of the traveling waves. Numerical simulations indicate that solutions of the model tend to form multidimensional patterns analogous to cells in gaseous detonations. |
| first_indexed | 2024-09-23T14:06:14Z |
| format | Article |
| id | mit-1721.1/103580 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T14:06:14Z |
| publishDate | 2016 |
| publisher | Society for Industrial and Applied Mathematics (SIAM) |
| record_format | dspace |
| spelling | mit-1721.1/1035802022-10-01T19:14:28Z Study of a Model Equation in Detonation Theory: Multidimensional Effects Faria, Luiz Kasimov, A. R. Rosales, Rodolfo Massachusetts Institute of Technology. Department of Mathematics Faria, Luiz Rosales, Rodolfo We extend the reactive Burgers equation presented in [A. R. Kasimov, L. M. Faria, and R. R. Rosales, Phys. Rev. Lett., 110 (2013), 104104], [L. M. Faria, A. R. Kasimov, and R. R. Rosales, SIAM J. Appl. Math., 74 (2014), pp. 547--570] to include multidimensional effects. Furthermore, we explain how the model can be rationally justified following the ideas of the asymptotic theory developed in [L. M. Faria, A. R. Kasimov, and R. R. Rosales, J. Fluid Mech., 784 (2015), pp. 163--198]. The proposed model is a forced version of the unsteady small disturbance transonic flow equations. We show that for physically reasonable choices of forcing functions, traveling wave solutions akin to detonation waves exist. It is demonstrated that multidimensional effects play an important role in the stability and dynamics of the traveling waves. Numerical simulations indicate that solutions of the model tend to form multidimensional patterns analogous to cells in gaseous detonations. King Abdullah University of Science and Technology (KAUST) National Science Foundation (U.S.) (NSF grant DMS-1115278) National Institutes of Health (U.S.) (NSF grant DMS-1318942) 2016-07-12T19:07:20Z 2016-07-12T19:07:20Z 2016-05 2016-02 Article http://purl.org/eprint/type/JournalArticle 0036-1399 1095-712X http://hdl.handle.net/1721.1/103580 Faria, L. M., A. R. Kasimov, and R. R. Rosales. “Study of a Model Equation in Detonation Theory: Multidimensional Effects.” SIAM Journal on Applied Mathematics 76, no. 3 (January 2016): 887–909. © 2016, Society for Industrial and Applied Mathematics. https://orcid.org/0000-0002-8828-5930 https://orcid.org/0000-0002-8129-2548 en_US http://dx.doi.org/10.1137/15M1039663 SIAM Journal on Applied 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. application/pdf Society for Industrial and Applied Mathematics (SIAM) SIAM |
| spellingShingle | Faria, Luiz Kasimov, A. R. Rosales, Rodolfo Study of a Model Equation in Detonation Theory: Multidimensional Effects |
| title | Study of a Model Equation in Detonation Theory: Multidimensional Effects |
| title_full | Study of a Model Equation in Detonation Theory: Multidimensional Effects |
| title_fullStr | Study of a Model Equation in Detonation Theory: Multidimensional Effects |
| title_full_unstemmed | Study of a Model Equation in Detonation Theory: Multidimensional Effects |
| title_short | Study of a Model Equation in Detonation Theory: Multidimensional Effects |
| title_sort | study of a model equation in detonation theory multidimensional effects |
| url | http://hdl.handle.net/1721.1/103580 https://orcid.org/0000-0002-8828-5930 https://orcid.org/0000-0002-8129-2548 |
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