A simple finite volume method for the shallow water equations

We present a new finite volume method for the numerical solution of shallow water equations for either flat or non-flat topography. The method is simple, accurate and avoids the solution of Riemann problems during the time integration process. The proposed approach consists of a predictor stage and...

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Bibliographic Details
Published in:Journal of computational and applied mathematics Vol. 234; no. 1; pp. 58 - 72
Main Authors: Benkhaldoun, Fayssal, Seaïd, Mohammed
Format: Journal Article
Language:English
Published: Kidlington Elsevier B.V 01.05.2010
Elsevier
Subjects:
Dam-break problems
Exact sciences and technology
Finite volume scheme
Mathematical analysis
Mathematics
Measure and integration
Method of characteristics
Numerical analysis
Numerical analysis. Scientific computation
Partial differential equations
Partial differential equations, initial value problems and time-dependant initial-boundary value problems
Sciences and techniques of general use
Shallow water equations
Shallow water equations
Finite volume scheme
Method of characteristics
Dam-break problems
Integration
Riemann problem
Initial value problem
Finite volume method
Shallow water
Partial differential equation
Numerical analysis
Applied mathematics
Numerical solution
Analytical solution
ISSN:0377-0427, 1879-1778
Online Access:Get full text
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Summary:We present a new finite volume method for the numerical solution of shallow water equations for either flat or non-flat topography. The method is simple, accurate and avoids the solution of Riemann problems during the time integration process. The proposed approach consists of a predictor stage and a corrector stage. The predictor stage uses the method of characteristics to reconstruct the numerical fluxes, whereas the corrector stage recovers the conservation equations. The proposed finite volume method is well balanced, conservative, non-oscillatory and suitable for shallow water equations for which Riemann problems are difficult to solve. The proposed finite volume method is verified against several benchmark tests and shows good agreement with analytical solutions.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2009.12.005