Goal: Both to increase fuel efficiency and to reduce operating costs and pollutant emissions, continuous design improvements in combustion systems need to be introduced. Conventional propulsion systems utilized nowadays mostly rely on deflagration processes and several variants of the constant-pressure Brayton cycle. However, in thermodynamical terms, energy release under near constant volume conditions, as occurs in rotating detonation engines (RDEs), is more efficient than under constant-pressure ones. Although the advantages of detonation cycles over Brayton ones have been recognized for several decades, the former more efficient cycles have not been implemented yet in practical combustion systems operating in continuous flow operating mode. This occurs because there are several technical challenges that need to be overcome first, before safely and effectively using them in combustion systems relevant to propulsion applications. One of these challenges relates to the strong shock-turbulence-chemistry (STC) interactions occurring in such systems, which remain poorly understood. Accordingly, this project aims to propose new theoretical constructs for large eddy simulation (LES) sub-grid scale (SGS) models, which allow modeling shock-turbulence-chemistry interactions, accounting for deflagration-to-detonation transition (DDT) processes, and which are applicable in numerical simulations of rotating detonation engines. After proposed, the referred new theoretical constructs will be used to study physical processes in canonical flow configurations related to pressure-gain combustion systems and rotating detonation engines. Once the basic science questions are addressed, the possible application areas targeted with this project include rotorcraft and scramjets/ramjets for hypersonic propulsion, as well as aircraft and marine gas turbine-based engines. As such, it is expected that the outcomes from this project are utilized to design and use next generation, more compact, and efficient power plants.