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 developed for unstructured meshes. The numerical method combines many attractive features of the finite volume method and unstructured finite elements, however, inside the elements a finite difference scheme based on generalized coordinate transformations has been applied. The method of solution of the equations is a well developed pressure correction algorithm that has worked well previously for structured meshes. The physical applications in the paper include axisymmetry and two-dimensional problems, as well as variable density solutions of the Navier-Stokes equations. It is the authors' opinion that some of the methods developed in the paper may have been used by other investigators, however, we have not found references in the literature that explicitly use finite differences to solve flows on unstructured element based meshes. A major goal of the paper is to show some of the similarities between the 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 Elsevier Science Ltd. All rights reserved.