A sixth-order finite volume method for diffusion problem with curved boundaries |
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| Institution: | 1. University of Toulouse, UPS, INPT, Laplace, 118 route de Narbonne, F-31062 Toulouse cedex 9, France;2. Centre of Mathematics, University of Minho, Campus de Azurém, Guimarães 4080-058, Portugal;3. Institut de Mathématiques de Toulouse, Université Paul Sabatier, Toulouse 31062, France;4. CNRS, Laplace, Toulouse F-31062, France |
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| Abstract: | 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 domains 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 reconstruction 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. |
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