On the optimisation of discretising steps in the space and time domains along with over-relaxation parameter in the finite difference solution of the transient heat-flow equation
Optimisation of the discretising steps in the space and time domains has been studied for the evaluation of corresponding optimum value of over-relaxation parameter in the numerical solution of transient heat flow equation using successive-over-relaxation method in the finite difference code. No closed 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 discretising steps in the space and the time domains for an optimal over-relaxation parameter The maximum finite difference error and the number of iterations required to achieve a reasonable error tolerance in the functional value are the two criteria used to obtain an optimised set of parameters. The effect of deviation from the optimised values of any of the involved parameters has been shown over a model problem of one-dimensional diamond-IIa medium of 100 micrometer length and for a time duration of 1.24 micro-seconds.
optimisation finite differences transient flow