時空間領域数値解法「タイムスペース法」の計算性能改善に関する研究 : 熱工学,内燃機関,動力など

In this paper, computing performance of the Time-Space Method (TSM), which has been proposed as a high-speed solver for general heat transfer and fluid flow problems (Saitoh et al., 1994), was thoroughly improved. In the TSM calculations, the coordinate in the timewise direction was considered as one of coordinates in the spatial direction, thereby transforming an ordinary unsteady 3-D initial-value problem into a steady 4-D boundary-value problem. The TSM can take an arbitrary time step, and the time step is determined solely by the resolution in the timewise direction required for the solution and the degree of accuracy. The computing time will be reduced to 1/100th∼1/1000th of conventional schemes for 2-D or 3-D problems. However, in order to apply to three-dimensional larger scale problems, i.e., global warming, urban warming and general ocean circulation, an iterative method in four dimensions due to the TSM procedure shows slower convergence than that in lower dimensions. Motivated by this situation, we further improved the convergence of the TSM by incorporating some key ideas for a natural convection heat transfer problem in a 3-D cubical cavity. In addition, benchmark solutions were presented for validation of computing performance of other numerical schemes proposed.