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A generalized Rusanov method for Saint-Venant equations with variable horizontal density. (English) Zbl 1246.76065

Fořt, Jaroslav (ed.) et al., Finite volumes for complex applications VI: Problems and perspectives. FVCA 6, international symposium, Prague, Czech Republich, June 6–10, 2011. Vol. 1 and 2. Berlin: Springer (ISBN 978-3-642-20670-2/hbk; 978-3-642-20671-9/ebook). Springer Proceedings in Mathematics 4, 89-96 (2011).
Summary: 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.
For the entire collection see [Zbl 1220.76004].

MSC:

76M12 Finite volume methods applied to problems in fluid mechanics
35L04 Initial-boundary value problems for first-order hyperbolic equations
65N08 Finite volume methods for boundary value problems involving PDEs
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