Study of the Numerical Diffusion in Computational Calculations

Abstract

The numerical simulation of fluid flow and heat/mass-transfer phenomena requires the numerical solution of the Navier-Stokes and energy-conservation equations coupled with the continuity equation. Numerical or false diffusion is the phenomenon of inserting errors in the calculations that compromise the accuracy of the computational solution. The Taylor series analysis that reveals the truncation/discretization errors of the differential equations terms should not be termed as false diffusion. Numerical diffusion appears in multi-dimensional flows when the differencing scheme fails to account for the true direction of the flow. Numerical errors associated with false diffusion are investigated via two-and three-dimensional problems. A numerical scheme must satisfy necessary criteria for the successful solution of the convection-diffusion formulations. The common practice of approximating the diffusion terms via the central-difference approximation is satisfactory. Attention is directed to the convection terms since these approximations induce false diffusion. The equations of all the conservation equations in this study are discretized by the finite volume method.