Numerical simulation of supersonic flows around systems of free bodies

The problem of supersonic flow around a system of bodies freely moving in a gas flow is considered. The mathematical model consists of Euler's equations for a region filled with gas, supplemented by Newton's equations for describing the motion of rigid bodies under pressure force. The computational algorithm uses locally adaptive Cartesian grids, in which the adaptation is based on wavelet analysis. The interaction of gas and solids is modeled using the immersed boundary method. The capabilities of the software implemented code are demonstrated on the problem of raising a dust grain under the action of a shock wave and on modeling the free motion of a system of particles in a supersonic 2D gas flow. Quantitative and qualitative results on the velocity of a dust grain and on the evolution of initial bodies configurations are obtained, which refine the known results.