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

Patricia Cargo, Gérald Samba (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We consider the Pn 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 the P1 model...

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