Mathematical Modeling for Building Fire

Abstract

Theoretical and experimental numerical analysis have proposed the capable of being executed computational finite difference method for fire induced natural convective heat flow using the viscous heat conductive compressible fluid with K-e model in the fire compartment. Because two-point upwind difference scheme give the numerical viscosity, the computational results are different from the approximate solutions at the large velocity. The practical stability and the truncation errors for computing finite difference equations approximating fire governing equations have been introduced by theoretical numerical analysis. The sensitivities of numerical solutions have been evaluated by the theoretical and experimental numerical analysis. As the results of numerical experiments we proposed that the reasonable time interval and space mesh size are chosen considering the CPU time. Furthermore we have introduced the Re* for the equation of motion or Pe*for the equation of energy. We proposed that the values of Re* and Pe* indicate the trust in the approximate solutions in consequence of the numerical experiments.