The Finite Difference Method for transient convection-diffusion problems

Abstract

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.

Stamp forming optimization for formability and crystallinity

“…A coupled thermal and crystallization model, based on the explicit finite difference method was developed by employing the work of Majchrzak & Turchan [4]. The model is able to predict the temperature and crystallization evolution during the stamp forming process.…”

The Method of Lines With a Finite Volumes Approach for Transient Convection-Diffusion Problems

“…µρ λ = α Study of this problem without discontinuities of λ was done for instance in [7] and the authors use the finite difference method.…”