Investigation of Accelerating the Convergence of an Implicit Numerical Solution of Transient Heat Transfer Problems

摘要

This study investigates two methods of increasing the rate of convergence of the two dimensional five point implicit finite difference representation of the diffusion equation of transient heat transfer. The two methods are adapted Wegstein and successive overrelaxation. Various techniques of scanning the mesh system formed by the finite differences and an 'a priori' overrelaxation factor are also investigated. An example problem is used to determine that successive overrelaxation with a sophisticated technique of repeatedly scanning all boundary values of the problem into the finite difference mesh is the fastest system of those tested to solve the implicit simultaneous equations of this study. The solutions of twenty-eight (28) other problems by this same system show that an average of 35.2% savings in number of iterations to solution is realized by this system as compared to successive overrelaxation with a conventional repetitive scanning technique. An 'a priori' relaxation factor which is related to the maximum temperature gradients of the problem is obtained. This 'a priori' factor is within 10% of the optimum relaxation factors for all problems and is an accurate approximation for those problems without heat generation. (Author)