We conduct direct numerical simulations for clarifying the mechanics of high-speed flows in two-phase media with shock waves (e.g., shock wave interaction with a cloud or a layer of particles). We describe the interaction between the flow and particles by solving the Euler equations in a domain with variable boundaries. Cartesian grid methods (also known as cut-cell methods, immersed boundary methods) are the most appropriate class of numerical methods in this case. The work describes the development of an effective parallel computational algorithm for a Cartesian grid method and the application of the algorithm for simulating the relaxation of several interacting particles behind a passing shock wave corresponding to natural experiments.