The Sn discrete-ordinates method is used to find numerical solutions in a two-dimensional rectangular enclosure with a gray absorbing, emitting, and isotropically scattering medium. Results are obtained for the S2, S4, and S6 approximations that correspond to 4, 12, and 24 flux approximations, respectively, and are compared with exact solutions, numerical Hottel’s zone results, P3 differential approximations, and an approximation method developed by Modest. The S2 approximation solutions were found to be applicable only for several specific cases and are not recommended for general use. The S4 and S6 solutions compare favorably with other methods and can be used to predict radiant intensity and surface heat transfer rate for various surface and optical conditions.

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We present an adaptive projection method for modeling unsteady, low-Mach reacting flow in an unconfined region. The equations are based on a model for low-Mach number combustion that consists of evolution equations coupled with a constraint on the divergence of the flow. The algorithm is based on a projection methodology in which we first advance the evolution equations and then solve an elliptic equation to enforce the divergence constraint. The adaptive mesh refinement (AM R) scheme uses a time-varying hierarchy of rectangular grids. The integration scheme is a recursive procedure in which coarse grids are advanced, fine grids are advanced to the same time as the coarse grids, and the coarse and fine grid data are then synchronized.The method is currently implemented for laminar, axisymmetric flames with a reduced kinetics mechanism and a Lewis number of unity. Three methane-air flames, two steady and one flickering, are presented as numerical examples.

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