The Stability Of The Steady And Compressible Flow Which Contains Transonic Shock Wave

In this paper we study the problem that when the supersonic flow bypasses the solid angle which is surrounded by static gas whether the steady and compressible flow containing transonic shock wave is stable or not. If the pressure of the upstream flow meet certain conditions and less than that of the static gas, there may be an intense shock wave when the supersonic flow bypasses the solid angle to increase the pressure of the gas behind the shock wave. Also there exists a contact discontinuity in the downstream of the wave discontinuity to separate the subsonic flow and the static gas in the right and lower part of the solid angle. In this paper, the main task is to determine specific location of the strong shock wave and contact discontinuity and the airflow status in the subsonic regions. The main idea is to give the background solution of the physical problem a small perturbation. After the disturbance we study the stability of the compressible flow. The specific research methods are to give the two-dimensional steady compressible euler equations linear transformation, and transform the contact discontinuity into transverse axis, namely fix a free boundary first, and then use Rankine-Hugoniot conditions of another free boundary, dividing Rankine-Hugoniot conditions, conversing the free boundary value problem to a nonlinear fixed boundary value problem and an ordinary differential equation. Then use nonlinear iteration to linearize the fixed boundary value problem in the background solution. Estimate this linear fixed boundary value problem solution we can not only conclude that the stability of the compressible flow in small disturbance condition, but also determine the position of shock wave and contact discontinuity.