A New Numerical Method for Simulation of Low-Mach Combustion

The detailed numerical simulation of unsteady phenomena where there is strong coupling between momentum, mass an d energy transport, with source terms adding to the stiffness of the problem, generally requires huge computing resources. Many different methods were developed so far, some valid for steady-state problems [1,2], some suitable for unsteady simulations as well [3,4,5]. Progress in this field is achieved by development and refinement of models and methods, and by advances in computing speed. The latter are essentially foreseen through parallel architectures, and this certainly must influence the former. In this work, a new method is presented that is meant to be especially efficient in the numerica! simulation of low-Mach,low-Reynolds flows with strong thermal expansion due to heat transfer and/or chemical reactions. The mode! is based on the classic Navier-Stokes equations for reacting flows, with few simplifying assumptions which certainly apply to the cases mentioned. The equations are closed with proper constitutive equations determined by the nature of the gas mixture, and with proper initial and boundary conditions. The method is then derived by manipulating the balance equations following the approach originally developed by Harlow [6] for incompressible, non-reacting flows, here extended to compressible (in a restricted sense), reacting flows. Conventional methods developed for compressible flows solve for density as a main dependent variable (whose variatiqn explicitly appears in the continuity equation), and subsequently calculate pressure from the gas state equation. In our case, by expressing the pressure as p(x,t) = p0 (t )+ p1 (x,t) where p0 (t) =-/i J0 p(x,t)d0., it can be shown that, in the limit of Mach <