The transportive property and convective numerical stability of the steady-state convection-diffusion finite-difference equation

The propagation characteristics of a localized disturbance are studied for various discretized forms of a convective term using the method of discrete perturbation analysis. Convective numerical stability is achieved for each of the discretization schemes when the disturbance and its propagated effects at neighboring points have the same sign. The analysis allows determination of which of the schemes possesses the transportive property, and the relationship between the transportive property and convective numerical stability is shown. A method for determining whether a finite difference scheme for the convection-diffusion equation is stable or conditionally stable is presented.