MULTI-SPATIAL-TEMPORAL GRIDS FOR THREE-DIMENSIONAL TRANSIENT CONDUCTION PROBLEMS

Abstract

Computationally intensive problems are often encountered in numerical heat transfer studies. One of the major causes is the small time steps brought forth by the fine spatial grid required at critical regions. Consequently, computational efficiency becomes one of the key issues in such numerical studies. By and large, the existing methods for enhancing computational efficiency either are applicable only for iterative operations, or provide limited speed-up because the solutions at certain regions within the domain are marching with an unnecessarily small time step. This work presents the development of a new method that achieves higher computational efficiency. This method is herein referred to as the Multi-Spatial-Temporal Grid (MSTG) method, and it provides a significant speed-up by simultaneously implementing grid reduction and multiple time steps. This method has been tested to be effective in improving the computational efficiency of conduction problems in transient, multidimensional orthogonal coordinates. Current benchmarking showed the solution obtained from this method to be within 0.04% of those obtained from a uniform grid. In addition, the speed-up of this scheme was found to be significantly higher than with most existing methods.