Implicit preconditioning method for turbulent reacting flows

An implicit scheme for the simulation of turbulent chemically reacting flows at all Mach numbers is presented and applied to test problems. The approach is based on the TASCOM-3D code developed for supersonic combustion calculations. It employs a cell centered finite volume method with central differences, q-omega-turbulence closure and non-equilibrium chemistry. A new preconditioning matrix is introduced, which rescales the pressure terms at low Mach numbers to limit the condition number. It proves to be advantageous over other preconditioners concerning robustness and accuracy. A conservative formulation for artificial viscosity is used, coupled with the preconditioner. This is necessary to enable convergence and to improve the accuracy at low Mach numbers. The method is shown to work well for Mach numbers from as low as 0.001 up to supersonic speeds.