Numerical Simulation of Supersonic Flows around Systems of Free Bodies

摘要

The problem of a 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 the influence of pressure. 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 free boundary method. The capabilities of the software-implemented code are demonstrated on the problem of the rise of a dust grain under the action of a shock wave and on the simulation of the motion of a system of bodies in a two-dimensional supersonic flow of an inviscid gas. Quantitative and qualitative results are obtained on the velocity of a dust grain and on the evolution of the initial configurations of bodies, which refine the known results.