Paper Info
Title
Extension of WAF Type Methods to Non-Homogeneous Shallow Water Equations with Pollutant
Abstract
This paper deals with the extension of the WAF method to discretize Shallow Water Equations with pollutants. We consider two different versions of the WAF method, by approximating the intermediate waves using the flux of HLL or the direct approach of HLLC solver. It is seen that both versions can be written under the same form with different definitions for the approximation of the velocity waves. We also propose an extension of the method to non-homogeneous systems. In the case of homogeneous systems it is seen that we can rewrite the third component of the numerical flux in terms of an intermediate wave speed approximation. We conclude that--in order to have the same relation for non-homogeneous systems--the approximation of the intermediate wave speed must be modified. The proposed extension of the WAF method preserves all stationary solutions, up to second order accuracy, and water at rest in an exact way, even with arbitrary pollutant concentration. Finally, we perform several numerical tests, by comparing it with HLLC solver, reference solutions and analytical solutions.
Year
DOI
Venue
2008
10.1007/s10915-008-9185-9
J. Sci. Comput.
Keywords
Field
DocType
intermediate wave speed,intermediate wave speed approximation,waf type methods,non-homogeneous system,non-homogeneous shallow water equations,finite volume method · well-balanced · upwinding · shallow water · source terms · waf · hllc · pollutant,numerical flux,intermediate wave,proposed extension,waf method,different definition,hllc solver,different version,second order,shallow water,pollutant,analytic solution,finite volume method,upwinding,shallow water equation,source term
Waves and shallow water,Direct method,Discretization,Mathematical optimization,Mathematical analysis,Upwind scheme,Flux,Solver,Finite volume method,Mathematics,Shallow water equations
Journal
Volume
Issue
ISSN
36
2
1573-7691
Citations 
PageRank 
References 
5
0.61
9
Authors
2
Name
Order
Citations
PageRank
E. D. FernáNdez-Nieto1617.52
G. Narbona-Reina282.43