Well-Balanced bottom discontinuities treatment for high-order shallow water equations WENO scheme / Valerio Caleffi in Journal of engineering mechanics, Vol. 135 N° 7 (Juillet 2009)  

Public ISBD [article]  inJournal of engineering mechanics > Vol. 135 N° 7 (Juillet 2009) . - pp. 684-696 Titre : Well-Balanced bottom discontinuities treatment for high-order shallow water equations WENO scheme Type de document : texte imprimé Auteurs : Valerio Caleffi, Auteur ; Alessandro Valiani, Auteur Article en page(s) : pp. 684-696 Note générale : Mécanique appliquée Langues : Anglais (eng) Mots-clés : Shallow water Slopes Discontinuities. Résumé : A finite volume well-balanced weighted essentially nonoscillatory (WENO) scheme, fourth-order accurate in space and time, for the numerical integration of shallow water equations with the bottom slope source term, is presented. The main novelty introduced in this work is a new method for managing bed discontinuities. This method is based on a suitable reconstruction of the conservative variables at the cell interfaces, coupled with a correction of the numerical flux based on the local conservation of total energy. Further changes regard the treatment of the source term, based on a high-order extension of the divergence form for bed slope source term method, and the application of an analytical inversion of the specific energy-depth relationship. Two ad hoc test cases, consisting of a steady flow over a step and a surge crossing a step, show the effectiveness of the method of treating bottom discontinuities. Several standard one-dimensional test cases are also used to verify the high-order accuracy, the C-property, and the good resolution properties of the resulting scheme, in the cases of both continuous and discontinuous bottoms. Finally, a comparison between the fourth-order scheme proposed here and a well-established second-order scheme emphasizes the improvement achieved using the higher-order approach. DEWEY : 620.1 ISSN : 0733-9399 En ligne : http://ascelibrary.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=JENMDT000 [...] [article] Well-Balanced bottom discontinuities treatment for high-order shallow water equations WENO scheme [texte imprimé] / Valerio Caleffi, Auteur ; Alessandro Valiani, Auteur . - pp. 684-696. Mécanique appliquée Langues : Anglais (eng) in Journal of engineering mechanics > Vol. 135 N° 7 (Juillet 2009) . - pp. 684-696 Mots-clés : Shallow water Slopes Discontinuities. Résumé : A finite volume well-balanced weighted essentially nonoscillatory (WENO) scheme, fourth-order accurate in space and time, for the numerical integration of shallow water equations with the bottom slope source term, is presented. The main novelty introduced in this work is a new method for managing bed discontinuities. This method is based on a suitable reconstruction of the conservative variables at the cell interfaces, coupled with a correction of the numerical flux based on the local conservation of total energy. Further changes regard the treatment of the source term, based on a high-order extension of the divergence form for bed slope source term method, and the application of an analytical inversion of the specific energy-depth relationship. Two ad hoc test cases, consisting of a steady flow over a step and a surge crossing a step, show the effectiveness of the method of treating bottom discontinuities. Several standard one-dimensional test cases are also used to verify the high-order accuracy, the C-property, and the good resolution properties of the resulting scheme, in the cases of both continuous and discontinuous bottoms. Finally, a comparison between the fourth-order scheme proposed here and a well-established second-order scheme emphasizes the improvement achieved using the higher-order approach. DEWEY : 620.1 ISSN : 0733-9399 En ligne : http://ascelibrary.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=JENMDT000 [...]

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