A finite volume formulation of compact central schemes on arbitrary structured grids

In the present paper a formulation allowing the use of compact schemes in the finite volume context on arbitrary meshes is presented. The proposed formulation is based on the use of an implicit formula to evaluate the fluxes on the cell faces. A series of numerical experiments for a 2D model convection equation, a flat plate, a subsonic vortical problem as well as the LES simulation of channel flow has been carried out. The results indicate an important improvement in obtained accuracy compared to a standard central finite volume formulation.