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Finite volume scheme for convection-diffusion problems

H. Belhadj


This paper is devoted to the system of shallow water equations coupled to a transport equation. The obtained system of equations is of the convection diffusion type. The unstructured cell centred finite volume scheme is used for the discretization of the convection part. The MUSCL technique is applied to increase the accuracy of the scheme. The diffusion part of the system is discretized using a Green-Gauss interpolation technique based on diamond shaped co-volumes. Several applications in fluid dynamics were performed successfully. The test-case that is presented in this paper deals with the pollutant transport in a rectangular reservoir.


Shallow water equations, transport equation, convection, diffusion, Finite volume method, unstructured mesh, Roe scheme, Green Gauss interpolation.

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