A NATURAL EXTENSION OF THE CONVENTIONAL FINITE-VOLUME METHOD INTO POLYGONAL UNSTRUCTURED MESHES FOR CFD APPLICATION

A new general cell-centered solution procedure based upon the conventi onal control or finite volume (CV or FV) approach has been developed f or numerical heat transfer and fluid flow which encompasses both struc tured and unstructured meshes for any kind of mixed polygon cell. Unli ke conventional FV methods for structured and block structured meshes and both FV and FE methods for unstructured meshes, the irregular cont rol volume (ICV) method does not require the shape of the element or c ell to be predefined because it simply exploits the concept of fluxes across cell faces. That is, the ICV method enables meshes employing mi xtures of triangular, quadrilateral, and any other higher order polygo nal cells to be exploited using a single solution procedure. The ICV a pproach otherwise preserves all the desirable features of conventional FV procedures for a structured mesh; in the current implementation, c ollocation of variables at cell centers is used with a Rhie and Chow i nterpolation (to suppress pressure oscillation in the flow field) in t he context of the SIMPLE pressure correction solution procedure. In fa ct all other FV structured mesh-based methods may be perceived as a su bset of the ICV formulation. The new ICV formulation is benchmarked us ing two standard computational fluid dynamics (CFD) problems, i.e., th e moving lid cavity and the natural convection driven cavity. Both cas es were solved with a variety of structured and unstructured meshes, t he latter exploiting mixed polygonal cell meshes. The polygonal mesh e xperiments show a higher degree of accuracy for equivalent meshes (in nodal density terms) using triangular or quadrilateral cells; these re sults may be interpreted in a manner similar to the CUPID scheme used in structured meshes for reducing numerical diffusion for flows with c hanging direction.