Proposal of super time-saving method: Time-space method

In this paper, a super time-saving method (Time-space method: TSM) for general transient flow and heat transfer problems was proposed. In the proposed TSM, the timewise coordinate is incorporated into one of the spatial coordinates, thereby transforming usual transient 2-D(or 3-D) problems into steady 3-D (or 4-D) spatial problems. The initial and future equilibrium conditions are treated as the boundary conditions. The TSM has an outstanding feature that it can eliminate the so-called numerical instability since time integration is not necessary, which has been the biggest problem in the principal numerical methodologies in the past. Namely, no error propagation in the timewise direction occurs for the TSM. The TSM is applicable to almost all the transient heat transfer and flow problems including 3-dimensional freezing/melting, global warming, urban warming, large scale atmospheric and ocean circulations. The TSM will be also effective for other problems in the field of solid mechanics and so on. The computer running time will be drastically reduced to only 1/100th to approximately 1/1000th of the existing schemes for 2-D or 3-D problems. The sample calculations were presented for a two-dimensional melting problem in a square cavity and the validity of the present method was examined.