On the optimisation of discretising steps in the space and time domains along with over-relaxation parameter in the finite difference solution of thetransient heat-flow equation

Optimisation of the discretising steps in the space and time domains has be en studied for the evaluation of corresponding optimum value of over-relaxa tion parameter in the numerical solution of transient heat flow equation us ing successive-over-relaxation method in the finite difference code. No clo sed form solutions are available for the optimisation of a complete set of involved parameters in such problems. The present work deals quantitatively with the need for a more generalised closed form relation involving discre tising steps in the space and the time domains for an optimal over-relaxati on parameter The maximum finite difference error and the number of iteratio ns required to achieve a reasonable error tolerance in the functional value are the two criteria used to obtain an optimised set of parameters. The ef fect of deviation from the optimised values of any of the involved paramete rs has been shown over a model problem of one-dimensional diamond-IIa mediu m of 100 micrometer length and for a time duration of 1.24 micro-seconds.