A formally second-order cell centred scheme for convection-diffusion equations on general grids

• Published in: International journal for numerical methods in fluids 2013-03, Vol.71 (7), p.873-890
• Main Authors: Piar, L., Babik, F., Herbin, R., Latché, J.-C.
• Format: Article
• Language: English
• Subjects: Approximation; convection dominant regime; Convection-diffusion equation; convergence analysis; Diffusion; discrete maximum principle; finite volumes; Fluxes; Mathematical analysis; Mathematical models; Maximum principle; MUSCL method; Reconstruction
• ISSN: 0271-2091; 1097-0363
• DOI: 10.1002/fld.3688

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. We propose a finite volume scheme to compute the solution of the convection‐diffusion equation. The diffusive fluxes are approximated using a recent cell‐centred scheme, working on unstructured and possibly non‐conforming 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; the limitation does not involve any geometrical reconstruction, thus allowing the use of completely general grids, in any space dimension.