An adaptive projection method for unsteady, low-Mach number combustion

We present an adaptive projection method for modeling unsteady, low-Mach re acting flow in an unconfined region. The equations are based on a model for low-Mach number combustion that consists of evolution equations coupled wi th a constraint on the divergence of the flow. The algorithm is based on a projection methodology in which we first advance the evolution equations an d then solve an elliptic equation to enforce the divergence constraint. The adaptive mesh refinement (AMR) scheme uses a time-varying hierarchy of rec tangular grids. The integration scheme is a recursive procedure in which co arse grids are advanced, fine grids are advanced to the same time as the co arse 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.