A FINITE-VOLUME PROCEDURE TO SOLVE ELASTIC SOLID MECHANICS PROBLEMS IN 3-DIMENSIONS ON AN UNSTRUCTURED MESH

A Finite Volume (FV) procedure is described for solving the elastic so lid mechanics equations in three dimensions on an unstructured mesh, f or bodies undergoing thermal or mechanical loads. The, FV procedure is developed in parallel with the conventional FE Galerkin procedure so that the differences in each approach may be clearly distinguished. Th e matrix form of the FV procedure is described, and is implemented in parallel with the FE procedure, both for two-dimensional quadrilateral and three-dimensional brick meshes. The FV and FE procedures are then compared against a range of benchmark problems that test the basic ca pability of the FV technique. It is shown to be approximately as accur ate: as the FE procedure on similar meshes, though its system matrix s et-up time is twice as long for a node by node set-up procedure.