Application of the Precise Time Integration Method to Unsteady Heat Conduction Problems (Study of Accuracy and Practicality of the Precise Time Integration Method)

Abstract

A new numerical scheme, precise time integration (PTI) method was applied to unsteady heat conduction problems. The algorithm of the PTI method and the way to create coefficient matrices and vectors for the unsteady heat conduction problems were described in detail in this paper. The comparison between the PTI and the ordinary finite difference methods showed that the PTI method's solutions for one and two-dimensional heat conduction problems were more accurate than those of ordinary methods for a wide range of mesh Fourier number f. The comparison also showed that the PTI method needed larger memory capacity and longer time for calculations than the ordinary methods did.