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A formally second‐order cell centred scheme for convection–diffusion equations on general grids
Author(s) -
Piar L.,
Babik F.,
Herbin R.,
Latché J.C.
Publication year - 2012
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.3688
Subject(s) - convection–diffusion equation , finite volume method , mathematics , convection , grid , laplace transform , convergence (economics) , scheme (mathematics) , unstructured grid , diffusion , mathematical analysis , geometry , mechanics , physics , economics , thermodynamics , economic growth
SUMMARY We propose, in this paper, a finite volume scheme to compute the solution of the convection–diffusion equation on unstructured and possibly non‐conforming grids. The diffusive fluxes are approximated using the recently published SUSHI scheme in its cell centred version, that reaches a second‐order spatial convergence rate for the Laplace equation on any unstructured two‐dimensional/three‐dimensional grids. As in the MUSCL method, the numerical convective fluxes are built with a prediction‐limitation process, which ensures that the discrete maximum principle is satisfied for pure convection problems. The limitation does not involve any geometrical reconstruction, thus allowing the use of completely general grids, in any space dimension. Copyright © 2012 John Wiley & Sons, Ltd.