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

作者：Piar L; Babik F; Herbin R; Latche J C^*

来源：International Journal for Numerical Methods in Fluids, 2013, 71(7): 873-890.

DOI：10.1002/fld.3688

• finite volumes
• MUSCL method
• convection dominant regime
• discrete maximum principle
• convergence analysis

We propose, in this paper, a finite volume scheme to compute the solution of the convectiondiffusion 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.

• 出版日期2013-3-10