Abstract
We present a class of finite volume methods for the numerical solution of Saint-Venant equations with variable horizontal density. The model is based on coupling the Saint-Venant equations for the hydraulic variables with a suspended sediment transport equation for the concentration variable. To approximate the numerical solution of the considered models we propose a generalized Rusanov method. The method is simple, accurate and avoids the solution of Riemann problems during the time integration process. Using flux limiters, a second-order accuracy is achieved in the reconstruction of numerical fluxes. The proposed finite volume method is well-balanced, conservative, non-oscillatory and suitable for Saint-Venant equations for which Riemann problems are difficult to solve. The numerical results are presented for two test examples.
MSC2010: 35L04, 65N08, 76L05
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© 2011 Springer-Verlag Berlin Heidelberg
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Benkhaldoun, F., Mohamed, K., Seaïd, M. (2011). A Generalized Rusanov method for Saint-Venant Equations with Variable Horizontal Density. In: Fořt, J., Fürst, J., Halama, J., Herbin, R., Hubert, F. (eds) Finite Volumes for Complex Applications VI Problems & Perspectives. Springer Proceedings in Mathematics, vol 4. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20671-9_10
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DOI: https://doi.org/10.1007/978-3-642-20671-9_10
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