HIGHER-ORDER NUMERICAL-MODEL FOR SIMULATION OF TIME-DEPENDENT VARIABLE-DENSITY FLOWS

A numerical model, first-order accurate in time discretization and sec ond-order accurate in space discretization, is presented for the simul ation of time-dependent laminar diffusion flames. The numerical model uses a semiimplicit scheme for time marching and incorporates flux-cor rected transport (FCT) for convection terms and projection method for velocity-pressure coupling. A direct solver: is used for solving the p ressure Poisson equation. A time-splitting method is adopted to split the transport equation into a convection equation in explicit form and a diffusion equation in implicit form. The explicit convection equati on allows for implementation of the FCT without introducing an artific ial viscosity. The implicit diffusion equation removes the time step s ize restriction of the von Neumann stability criterion. Theoretical as sessments are derived for the order of accuracy of time difference by viewing the projection method as a lower-upper decomposition, and form ulation is also given to establish the second-order accuracy. The curr ent numerical model is used to solve the Smith-Hutton problem and the Burke-Schumann diffusion dame with or without external forcing of the fuel jet. Tile results are compared with solutions using the schemes o f lower-order accuracy in the space discretization. The comparison sho ws that significant numerical diffusion error exists in the solution w hen a first-order upwind difference scheme or power-law approximation is used. The present study suggests that a higher-order space differen ce scheme should be used for the simulation of time-dependent laminar jet diffusion dames, although a first-order time difference scheme wou ld be adequate.