Fire Safety Science Digital Archive

In numerical analysis for the fire mathematical models, the numerical spurious oscillations appear in the results which are computed by most of the traditional numerical methods such as the first order accuracy upwind difference scheme and the third order accuracy upwind difference scheme. The new numerical scheme is applied to PDEs with convection terms in the fire mathematical models. This scheme is based on switching high accurate interpolation of the profile to one satisfying the TVD condition for space variable over a local area when the numerical spurious oscillations is appeared. In this paper, we propose the new scheme, TVDCIP(Total Variation Diminishing Cubic Interpolated Propagation), that consists of the spatial interpolation and the mathematical algorithm for switching scheme with high order accuracy. TVDCIP method is applied to solve the nonlinear hyperbolic partial differential equations numerically such as Navier-Stoke’s type equations.