The Finite Difference Method for transient convection-diffusion problems

Abstract

The convection-diffusion equation (1D problem) is considered. At first, the unknown temperature T is expanded into a Taylor series with respect to time taking into account its three components. Next, using the convection-diffusion equation and equation obtained from the differentiation of this equation, the way of temperature T computations is shown. In this new equation the high order derivatives with respect to spatial co-ordinate appear and the approximation of these derivatives is also discussed. The explicit scheme is used and the stability criteria are formulated. Finally, the results of computations are shown.