TRUNCATION ERROR ANALYSIS OF THE FINITE VOLUME METHOD FOR A MODEL STEADY CONVECTIVE EQUATION

A fundamental error relation inherent in the Gauss divergence theorem provided the basis for studying the truncation error of the finite volume method with cell center formulation for a model steady convective equation. The consistency of the classical first- and second-order upwind schemes are proved to be seriously dependent on the grid distribution. If the simple nature of the finite volume method is retained, it is found that a consistent scheme for convective terms can not avoid the dissipation due to grid nonuniformity. The geometrical interpretation of the diffusive terms such as VZO are undertaken. Classical finite volume methods, which average an undefined 0 from its neighbouring nodes, are shown to introduce false fluxes whenever grid nonuniformity is present. A simple modification is proposed to cancel the false fluxes. Two test cases for the Laplace equation illustrate the applicability of the proposed scheme. However, even with this modified scheme, the consistency problem of the diffusion term is found to be seriously dependent on the grid uniformity. © 1992.