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TitleA sixth-order finite volume method for diffusion problem with curved boundaries,
Author(s)Boularas A
Clain, Stéphane
Baudoin, fulbert
Keywordsfinite volume
curved domain
Polynomial reconstruction
Poisson equation
Curved boundary
Issue date2017
JournalApplied Mathematical Modelling
Abstract(s)A sixth-order finite volume method is proposed to solve the Poisson equation for two- and three-dimensional geometries involving Dirichlet condition on curved boundary do- mains where a new technique is introduced to preserve the sixth-order approximation for non-polygonal or non-polyhedral domains. On the other hand, a specific polynomial recon- struction is used to provide accurate fluxes for elliptic operators even with discontinuous diffusion coefficients. Numerical tests covering a large panel of situations are addressed to assess the performances of the method.
Publisher version
AccessRestricted access (UMinho)
Appears in Collections:CMAT - Artigos em revistas com arbitragem / Papers in peer review journals

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