AbstractThe development and application of numerical simulation to the study of gas-dynamic processes occurring in solid-propellant rocket motors (SPRMs) is discussed. A characteristic feature of internal flows in the SPRM channels and nozzles is the presence of the condensed phase of nonspherical particles. Mathematical problems in this area feature the simultaneous occurrence of processes on many time and spatial scales, which describe the formation of agglomerate particles, their combustion, and transport in a flow of combustion products in internal channels and nozzles. A multilevel multiscale technique that combines models describing the state of the system at the micro-, meso-, and macroscales is the approach used to solve these problems. An overview of models varying in complexity and level of detail is given. The construction of multiscale models is considered in relation to the simulation of two-phase flows with metal-oxide agglomerates formed in the propellant channel and representing drops of molten metal with oxide particles attached to their surface. The options of the developed approach are demonstrated by the calculations of flows of combustion products containing agglomerate particles in the channels and nozzles of propulsion systems.