SOLUTION OF THE NAVIER-STOKES EQUATION WITH FINITE-DIFFERENCES ON UNSTRUCTURED TRIANGULAR MESHES

A low Mach number model of the Navier-Stokes equations has been develo ped for unstructured meshes. The numerical method combines many attrac tive features of the finite volume method and unstructured finite elem ents, however, inside the elements a finite difference scheme based on generalized coordinate transformations has been applied. The method o f solution of the equations is a well developed pressure correction al gorithm that has worked well previously for structured meshes. The phy sical applications in the paper include axisymmetry and two-dimensiona l problems, as well as variable density solutions of the Navier-Stokes equations. It is the authors' opinion that some of the methods develo ped in the paper may have been used by other investigators, however, w e have not found references in the literature that explicitly use fini te differences to solve flows on unstructured element based meshes. A major goal of the paper is to show some of the similarities between th e finite element and the difference methods that are both very popular at the present time. It is hoped that these similarities will lead to better understanding and improvements in both techniques. (C) 1998 El sevier Science Ltd. All rights reserved.