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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...
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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