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<datestamp>2017-12-21</datestamp>
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<publisher>HAL CCSD</publisher>
<title lang=en>A Split Godunov Scheme for Solving One-Dimensional Hyperbolic Systems in a Nonconservative Form</title>
<creator>Mophou, Gisèle Massengo</creator>
<creator>Poullet, Pascal</creator>
<contributor>Département de Mathématiques et Informatique (D.M.I.) ; Université des Antilles et de la Guyane (UAG) - Université des Antilles (Pôle Guadeloupe) ; Université des Antilles (UA) - Université des Antilles (UA)</contributor>
<contributor>Laboratoire de Mathématiques Informatique et Applications (LAMIA) ; Université des Antilles et de la Guyane (UAG)</contributor>
<description>International audience</description>
<source>ISSN: 0036-1429</source>
<source>SIAM Journal on Numerical Analysis</source>
<publisher>Society for Industrial and Applied Mathematics</publisher>
<identifier>hal-00770266</identifier>
<identifier>https://hal.univ-antilles.fr/hal-00770266</identifier>
<source>https://hal.univ-antilles.fr/hal-00770266</source>
<source>SIAM Journal on Numerical Analysis, Society for Industrial and Applied Mathematics, 2006, 40 (1), pp.1-25. 〈10.1137/S0036142900378637〉</source>
<identifier>DOI : 10.1137/S0036142900378637</identifier>
<relation>info:eu-repo/semantics/altIdentifier/doi/10.1137/S0036142900378637</relation>
<language>en</language>
<subject lang=en>Riemann solver</subject>
<subject lang=en>Burgers's equation</subject>
<subject lang=en>splitting method</subject>
<subject lang=en>Godunov scheme</subject>
<subject lang=en>nonconservative system</subject>
<subject>[INFO.INFO-NA] Computer Science [cs]/Numerical Analysis [cs.NA]</subject>
<type>info:eu-repo/semantics/article</type>
<type>Journal articles</type>
<description lang=en>In this paper, we developed a theoretical study for nonconservative sytems in one dimension in order to construct numerical schemes for solving the Riemann problem. The nonconservative form of our model system required the use of a well-adapted theory in order to give us a sense of our problem. We chose a framework of generalized functions for solving a scalar hyperbolic equation with a discontinuous coefficient $sigma_t +usigma_x approx 0$, where u is the velocity solution of a Burgers's equation. After an explicit solution of the Riemann problem, we derived Godunov split schemes for computing an approximate solution of the Cauchy problem. We applied our study to a system modeling elasticity and a system modeling gas dynamics. Some stability properties of a scheme and its convergence to a generalized solution are proved for the first model. Numerical experiments confirmed this convergence result. For the second model, calculations of flows containing weak-to-moderate shocks showed that conservation errors are reduced when the mesh is refined but were not entirely eliminated.</description>
<date>2006-07-26</date>
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