A formally second order cell centered scheme for convection-diffusion equations on unstructured non-conforming grids

Libuse Piar (1) , Fabrice Babik (1) , Raphaele Herbin (2) , Jean-Claude Latché (1)

1 IRSN - Institut de Radioprotection et de Sûreté Nucléaire
2 LATP - Laboratoire d'Analyse, Topologie, Probabilités

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.

Mots clés: Finite Volumes; MUSCL method; Convection dominant regime; Discrete maximum principle; Convergence analysis

Domaines: Analyse numérique [math.NA]

Libuse Piar, Fabrice Babik, Raphaele Herbin, Jean-Claude Latché. A formally second order cell centered scheme for convection-diffusion equations on unstructured non-conforming grids. International Journal for Numerical Methods in Fluids, 2013, 71 (7), pp.873:890. ⟨10.1002/fld.3688⟩. ⟨hal-00556911v2⟩