A well-balanced scheme for the numerical processing of source terms in hyperbolic equations
SIAM Journal on Numerical Analysis
On WAF-type schemes for multidimensional hyperbolic conservation laws
Journal of Computational Physics
Journal of Computational Physics
The surface gradient method for the treatment of source terms in the shallow-water equations
Journal of Computational Physics
ADER: A High-Order Approach for Linear Hyperbolic Systems in 2D
Journal of Scientific Computing
A Fast and Stable Well-Balanced Scheme with Hydrostatic Reconstruction for Shallow Water Flows
SIAM Journal on Scientific Computing
Journal of Computational Physics
ADER schemes for three-dimensional non-linear hyperbolic systems
Journal of Computational Physics
TVD Fluxes for the High-Order ADER Schemes
Journal of Scientific Computing
Journal of Computational Physics
ADER schemes for the shallow water equations in channel with irregular bottom elevation
Journal of Computational Physics
SIAM Journal on Scientific Computing
Mathematical and Computer Modelling: An International Journal
A Well-balanced Finite Volume-Augmented Lagrangian Method for an Integrated Herschel-Bulkley Model
Journal of Scientific Computing
Journal of Computational Physics
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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.