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Pré-Publication, Document De Travail Année : 2023

A positive and asymptotic preserving finite volume scheme for the linear transport equation on two dimensional unstructured meshes

Clément Lasuen
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Résumé

In this paper, we propose a finite volume scheme for the linear transport equation in two space dimensions. This scheme is based on an upwind scheme where the velocity is modified so as to recover the correct diffusion limit. The resulting scheme is \emph{asymptotic preserving}, positive under a classical $CFL$ condition and conservative. We propose a reconstruction procedure so as to make it second order consistent on unstructured polygonal meshes.
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Dates et versions

hal-04336178 , version 1 (11-12-2023)
hal-04336178 , version 2 (13-05-2024)

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  • HAL Id : hal-04336178 , version 2

Citer

Clément Lasuen. A positive and asymptotic preserving finite volume scheme for the linear transport equation on two dimensional unstructured meshes. 2024. ⟨hal-04336178v2⟩

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