Assessment of Stiff Integration Methods for Supersonic Combustion

Efficient time integration methods are required to resolve a large range of timescales associated with detailed chemical kinetics models for high-speed propulsion systems, which introduce numerical stiffness. Strang splitting separates these small timescales associated with chemistry from larger convective timescales. Several stiff time integration methods for solving first-order ordinary differential equations are implemented within the framework of a finitevolume solver, US3D, to be tested for their feasibility. A scaling test case is developed to understand the relative cost of these methods as the number of reactions and number of species is increased. The test case controls the stiffness of the problem relative to timescales observed within supersonic combustion cases. Initialization of the scaling problem provides insight as to how each stiff solver performs within different reaction regimes, such as relatively frozen gas zones and high reaction zones. These same stiff solvers are then applied within an Implicit Large-Eddy Simulation for a supersonic cavity using Strang splitting. The influence of the chemical model on the flame structure is compared with the use of a detailed reduced model and a quasi-global model. Temperature and heat release statistics are two main quantities of interest for study based on the role of chemistry within the reacting shear layer. Higher-order chemistry solvers show good agreement with fully coupled implicit solvers with beneficial computational costs.