Non reflecting boundary conditions for reacting flows

In this paper we explore the specification of time dependent boundary conditions suitable for the simulation of low Mach number reacting flows. The standard treatments used to date are based on the method of characteristics, and essentially set to zero the incoming characteristics; this practise has been shown to have deleterious effects on the flow evolution. The new approach, while still based on the method of characteristics, circumvents this problem through the application of a double expansion in terms of an appropriately defined Mach number. In the method, a low Mach number expansion of the dependent variables is coupled to a two-length scale decomposition. Through the double expansion, it is possible to separate inertial events (i.e. those moving at the local convection velocity) from acoustic events (those moving at the local sound speed). The paper highlights why previous treatments have encountered difficulties in turbulent flows, and provides a method by which heat release effects can be incorporated into a non-reflecting boundary condition framework. The accuracy of the method is demonstrated using a curved stagnating flame, in which the reaction zone crosses the boundary