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, for three-dimensional (3D) supersonic air and propane-air flows in channels of variable square cross section. The flows inside and outside the rotating elliptical cylinder, inside helical 3D channel of elliptic cross section were investigated. Specific features of shock-wave processes that are associated with the piston effect and focusing are established. The hypersonic analogy between planar and spatial flows is confirmed, which allows one to use 2D solutions in estimating 3D 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.