Numerical simulation of unsteady flows with transient regimes

Self-oscillatory flows in aerodynamics and astrophysics are studied. The two-dimensional compressible gas equations are solved using the implicit Runge–Kutta scheme of the third order with respect to the inviscid terms and of the second order with respect to the viscous terms. An algebraic Cebeci–Smith turbulence model is used. Weakly unsteady and strongly unsteady flow regimes are observed. The former occur in a supersonic flow past a cylinder with a front projection and in the heliosphere. Such flows became stable when the turbulent diffusion is taken into account. The latter flows occur when a supersonic jet meets an obstacle and when such a jet penetrates a cavity. In these flows, the amplitude of oscillations slightly decreases when the turbulent diffusion is taken into account.