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

Abderrhramane Boularas (1) , Stéphane Clain (2, 3) , Fulbert Baudoin (4)

1 LAPLACE - LAboratoire PLasma et Conversion d'Energie
2 IMT - Institut de Mathématiques de Toulouse UMR5219
3 CMAT - Centro de Matemática [Minho]
4 LAPLACE-DSF - Diélectriques Solides et Fiabilité

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.

Mots clés: Finite Volume; high-order; convection-diffusion; polynomial reconstruction; Poisson equation; curved boundary.

Domaines: Analyse numérique [math.NA]

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⟩