An Investigation of Convergence Techniques for Implicit Numerical Solution of the Diffusion Equation for Transient Heat Transfer

摘要

This study investigates the practical application of two convergence techniques designed to increase the rate of convergence of the method of successive displacements for the implicit numerical solution of the diffusion equation of transient nest transfer, A sample problem of determining the temperature distribution in a cube with a constant internal neat source and fixed boundary temperatures is solved to provide the necessary data.nThe results provide a theoretieel basis for the adapted degstein teennioue that was not previously available. this theoretical basis brings to light the feet that successive over relaxation and the adapted degstein technique are cased on the same theoretical background.nA procedure based on estimating the maximum elgen value of the method of successive displacements is used to make an approximation of the relaxation factor for successive over relaxation. This procedure is shown to be a practical method of finding the proper relaxation factor to estimate the difficult-to-determine optimum factor. The savings using this procedure was about 50% of the iterations required to obtain the same solution by successive displacements. A comparison of the two accelerating techniques is made. Items of comparison are: the number of iterations