Characterization of Smoke-Motion in the Buiding Fire (II)Numerical Solutions of the Heat-Fow Pattern in the Fire
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We shall treat the problem of a two-dimensional heat-flow of a viscous imcompresible fluid within a spuare cross section at the building fire. The governing epuations are continuity, motion and energy. Here the equation of motion is used to Navier-Stokes' law and Boussinesp approximation. The numerical solutions of these equations are studied, that various methods are carried out on a digital computer. For investigating the mathematical and camputational stability of finite difference epuations, moreover, the physical phenomena and computational technipue, a finite-difference method is applied to solve these epuations numerically. Attempt to solve partial differential epuations by finite-difference method forused to digital computer; 1] finite difference approximations toi) stability ii) convergence iii) rate of convergence iv) truncation error v) mathematical and numerical error2] Calculational solutions toi) calculated real time (CPU-time) ii) numerical methods for computer memory scale iii) rounding off error iv) elapsed time3] physical treatment toi) physical conservation of the epuations by the computational values ii) apropriate to numerical values for physical investigationiii) simulational modelsIn this paper, a finite difference epuation is reduced to a partial differential epuation by the backward implicit scheme and, central and upstream difference scheme. A simultaneous linear algebraic epuations by thismethod is solved by the succesive overrelaxation (S.O.R.) method with overrelaxation facter σ ΔT/X 2 (σ is nondimensionalcoefficient), where matrices are used Sparse Matrix out of the computer memory scale. Initial and boundary values difined by the experiment, and this problem was solved on the IBM SYSTEM/370 Model 135-DHO for Re=104, Gr=108 and Pr=0.72With this parameter values except for ε=10, CPU-time was about 28 min. and elapsed time about 32 min. to depict the motion of heat flow during 7 min. than a initiation used compiler is PL/I (F).
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