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.
Keywords
MSC2010: 35L04, 65N08, 76L05
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Mohamed, K.: Simulation numérique en volume finis, de problémes d’écoulements multidimensionnels raides, par un schéma de flux á deux pas. Dissertation, University of Paris 13, (2005)
Rusanov, V.: Calculation of interaction of non-steady shock waves with obstacles. Comp. Math. Phys. USSR. 1, 267–279 (1961)
Leighton, F.Z. Borthwick, A.G.L. Taylor, P.H.: 1-D numerical modelling of shallow flows with variable horizontal density. International Journal for Numerical Methods in Fluids. 62, 1209–1231 (2010)
Randall, J.L.: Numerical Methods for Conservation Laws, Lectures in Mathematics. ETH Zürich, (1992)
Roe, P.: Approximate riemann solvers, parameter vectors and difference schemes. J. Comp. Physics. 43, 357–372 (1981)
Sweby, P.K.: High resolution schemes using flux limiters for hyperbolic conservation laws. SIAM J. Numer. Anal. 21, 995–1011 (1984)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
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
Download citation
DOI: https://doi.org/10.1007/978-3-642-20671-9_10
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-20670-2
Online ISBN: 978-3-642-20671-9
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)