Pré-Publication, Document De Travail Année : 2011

A very high-order finite volume method for the one dimensional convection diffusion problem

Résumé

A new finite volume method for one dimensional convection diffusion problems is designed. The scheme is based on the Polynomial Reconstruction Operator (PRO-scheme) where a 5-degree polynomial representation is provided for each cell using the mean-values of the neighboring cells. Convective and diffusive numerical fluxes derive from the polynomial reconstruction and lead to a finite volume scheme of sixth-order of accuracy. Numerical examples are proposed to show the effectiveness of the method and the ability to manage the convection and the diffusion independently, {\it i.e.} the scheme is still functional even with vanishing viscosity.

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Dates et versions

hal-00653968 , version 1 (20-12-2011)

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  • HAL Id : hal-00653968 , version 1

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Stéphane Clain, Gaspar Machado, Rui M. S. Pereira. A very high-order finite volume method for the one dimensional convection diffusion problem. 2011. ⟨hal-00653968⟩
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