Numerical Simulations of Supersonic Multi-Component and Reacting Flows: Towards Combustion in a Supersonic Cavity

In this work, high-resolution numerical methods are extended to large-eddy simulation of supersonic, multi-component reacting flows and applied to a cavity combustion chamber configuration. Convective fluxes are discretized using the Gradient-Based Reconstruction method with monotonicity-preserving limiting for shock capturing, while viscous fluxes are computed using an α-damping scheme. These methods are extended to chemically reacting flows for the first time, using a fully GPU-resident implementation, with an explicit fifthorder Runge–Kutta–Cash–Karp (RKCK) scheme and adaptive time-step control for integration of the stiff chemical source terms. The methodology is first validated using the reacting shock–hydrogen bubble interaction, demonstrating accurate capture of material interfaces, shock-inducedmixing, and unsteady combustion dynamics. The approach is then applied to supersonic reacting flow in the University of Virginia Supersonic Combustion Facility (UVaSCF) cavity combustion chamber, where good qualitative agreement with experimental observations is obtained. The results demonstrate the ability of the proposed numerical framework to capture the coupled shock, mixing, and combustion phenomena characteristic of supersonic reacting flows, while enabling high-fidelity simulations at significantly reduced computational cost through full GPU acceleration.