A generalized Maccormack scheme for low Mach number, chemically-reacting large-eddy simulations

Chemically reacting flows contain a wide range of regimes with many velocity and time scales. The increasing access to computational resources enables higher-fidelity simulations of these flows. In order to take advantage of these capabilities, numerical schemes must be robust, efficient and accurate in all of the regimes present in the flow. Pressure-based schemes are suitable for many low Mach number flows, but are limited to low velocities and relatively small temperature variations. Density-based schemes struggle to converge in low-speed flows due to the time-step restrictions imposed by the acoustic velocity, which may be orders of magnitude larger than the convective velocity. Furthermore, such codes may exhibit excessive numerical dissipation due improper scaling of the dissipative properties of the scheme. Chemical reactions introduce another set of temporal scales associated with the kinetics mechanism used to model the system. These scales are often much smaller than the convective or acoustic scales and impose additional restrictions on the time-step. This disparity requires numerical schemes designed to handle the challenges that occur in low Mach number, chemically reacting flows. Analysis of density-based schemes at the low Mach number limit suggests that the development of improved, robust preconditioning with suitable operator splitting techniques leads to improved solution fidelity. In this work, a dual-time framework with low-Mach preconditioning is developed for complex, chemically reacting large-eddy simulations. A new version of the well-known MacCormack scheme is proposed and the resulting scheme improves the solution quality significantly at low Mach numbers. An established ordinary differential equation solver for stiff systems treats the stiffness associated with the chemical source terms. Methods to couple the PDE and ODE solvers in both pseudo-time and in physical time are proposed and analyzed. Validation of the non-reacting scheme and the coupled reacting scheme using canonical test cases demonstrates the improved solution fidelity and simulations of representative industrial applications demonstrate the combined scheme.Ph.D