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Resolution of the time dependent equations by a Godunov type scheme having the diffusion limit

Patricia Cargo;  Gérald Samba — 2010

ESAIM: Mathematical Modelling and Numerical Analysis

We consider the model to approximate the time dependent transport equation in one dimension of space. In a diffusive regime, the solution of this system is solution of a diffusion equation. We are looking for a numerical scheme having the diffusion limit property: in a diffusive regime, it has to give the solution of the limiting diffusion equation on a mesh at the diffusion scale. The numerical scheme proposed is an extension of the Godunov type scheme proposed by Gosse to solve...

An asymptotic preserving scheme for model using classical diffusion schemes on unstructured polygonal meshes

Emmanuel Franck;  Philippe Hoch;  Pierre Navaro;  Gérald Samba — 2011

ESAIM: Proceedings

A new scheme for discretizing the model on unstructured polygonal meshes is proposed. This scheme is designed such that its limit in the diffusion regime is the MPFA-O scheme which is proved to be a consistent variant of the Breil-Maire diffusion scheme. Numerical tests compare this scheme with a derived GLACE scheme for the system.

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