Mathematical modeling of shock-wave processes under gas solid boundary interaction

The results of numerical simulations are presented for planar air flows in a bounded volume of square cross section diminishing due to a uniform motion of the walls, for a flow of a propane-air mixture under sinusoidal variation of the size of the square domain, and for three-dimensional supersonic air and propane-air flows in channels of variable square cross section. Specific features of shock-wave processes that are associated with the piston effect and cumulation are established. The hypersonic analogy between planar and spatial flows is confirmed, which allows one to use two-dimensional solutions in estimating three-dimensional flows. The equations of a multicomponent ideal perfect gas and one-stage kinetics of chemical reactions are used to describe the flows. The method of numerical simulations is based on S.K. Godunov’s scheme and implemented within an original software package.