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

International audienceA 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