A physically consistent FVM interpolation scheme based on the discretized convection–diffusion equation

A physically consistent difference scheme is proposed to discretize the convection–diffusion equation in this paper. The interface variables of control volume are calculated by the interpolation of the discretized convection–diffusion equation rather than the direct interpolation with neighbor nodes in the direction perpendicular to the interface. In the new scheme, all the nodes of parallel and normal to the interface are involved, which means that the influence of cross-stream fluxes is considered. Obviously, the proposed interpolation scheme is full of physical meaning and better than the traditional convective interpolation schemes. Two simulations of typical benchmark problems, lid-driven cavity flow in square cavity and flow over a backward-facing step, are carried out with this scheme and some traditional schemes to prove the advantages of the proposed scheme.