An efficient splitting technique for two‐layer shallow‐water model |
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| Authors: | Christophe Berthon Françoise Foucher Tomás Morales |
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| Affiliation: | 1. Laboratoire de Mathématiques Jean Leray, CNRS UMR 6629, Université de Nantes, Nantes, France;2. Ecole Centrale de Nantes, 1 rue de la No?, BP 92101, Nantes cedex 3, France;3. Dpto. de Matemáticas, Universidad de Córdoba, Campus de Rabanales, Córdoba, Spain |
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| Abstract: | We consider the numerical approximation of the weak solutions of the two‐layer shallow‐water equations. The model under consideration is made of two usual one‐layer shallow‐water model coupled by nonconservative products. Because of the nonconservative products of the system, which couple both one‐layer shallow‐water subsystems, the usual numerical methods have to consider the full model. Of course, uncoupled numerical techniques, just involving finite volume schemes for the basic shallow‐water equations, are very attractive since they are very easy to implement and they are costless. Recently, a stable layer splitting technique was introduced Bouchut and Morales de Luna, M2AN Math Model Numer Anal 42 (2008), 683–698]. In the same spirit, we exhibit new splitting technique, which is proved to be well balanced and non‐negative preserving. The main benefit issuing from the here derived uncoupled method is the ability to correctly approximate the solution of very severe benchmarks. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1396–1423, 2015 |
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| Keywords: | two‐layer shallow‐water model finite volume schemes source term approximations splitting schemes well‐balanced schemes non‐negative preserving schemes |
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