AN INVESTIGATION OF CONVERGENCE TECHNIQUES FOR IMPLICIT NUMERICAL SOLUTION OF THE DIFFUSION EQUATION FOR TRANSIENT HEAT TRANSFER
AIR FORCE INST OF TECH WRIGHT-PATTERSON AFB OH
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The practical application of two convergence techniques designed to increase the rate of convergence of the method of successive displacements Gauss-Siedel for the implicit numerical solution of the diffusion equation of transient heat transfer is investigated. A sample problem of determining the temperature distribution in a cube with a constant internal heat source and fixed boundary temperatures is solved to provide the necessary data. The results provide a theoreticas for the adapted Wegstein technique. This theoretical basis brings to light the fact that successive overrelaxation and the adapted Wegstein technique are based on the same theoretical background. A procedure based on estimating the maximum eigenvalue of the method of successive displacements is used to make an approximation of the relaxation factor for successive overrelaxation.