Article Dans Une Revue Applied Mathematical Modelling Année : 2017

A sixth-order finite volume method for diffusion problem with curved boundaries

Résumé

A sixth-order finite volume method is proposed to solve the Poisson equation for two- and three-dimensional geometries involving curved boundaries. A specific polynomial reconstruction is used to provide accurate fluxes for diffusive operators even with discontinuous coefficients while we introduce a new technique to preserve the sixth-order approximation for non-polygonal domains. Numerical tests covering a large panel of situations are addressed to assess the performances of the method.

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hal-01052517 , version 1 (05-08-2014)

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Abderrhramane Boularas, Stéphane Clain, Fulbert Baudoin. A sixth-order finite volume method for diffusion problem with curved boundaries. Applied Mathematical Modelling, 2017, 42, pp.401-422. ⟨10.1016/j.apm.2016.10.004⟩. ⟨hal-01052517⟩
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