Mass-Flux-Based Implicit Multigrid Method for Modeling Multidimensional Combustion

Abstract

A highly accurate and ef cient method for modeling three-dimensional reacting ows with detailed chemistry is described in this paper. A mass-ux-based governing system is developed for general curvilinear coordinates to obtain compactness of the discretization stencil. The momentum equations are represented by a set of equations of mass uxes across cell interfaces, which are discretized by using staggered grid techniques. A third-order monotone upwind-biased scheme is used for all of the convection terms in the ow equations and species equations to minimize numerical diffusion and capture the sharp gradients existing in ames. The governing equations are divided into a chemical reaction part and a uid ow part, and they are solved in a semicoupled way. An implicit semicoarsening multigrid method combined with a line-distributive relaxation is used as the ow solver. The species equations are discretized by an implicit method and solved in a fully coupled way. Computational results for a con ned co owing diffusion ame show good agreement with experimental data. A detailed three-dimensional calculation of combustion in a gas-turbine combustor with strong swirling in ows is also presented.

An Implicit Multigrid Method for the Simulation of Chemically Reacting Flows

“…Slomski et al [17] and Radespiel et al [18] calculated reacting or dissociating air with small reaction schemes using standard multigrid procedures. Liao et al [19][20][21] employed the multigrid technique for the momentum equations only without proving convergence accelerations. Considerable speedups are obtained by Sheffer et al [22] for detonation waves using a two-level multigrid method.…”