Tsd Equations Of Shock Wave Reflection Structure

The problems of shock wave reflection and the nonlinear wave configuration of shock wave reflection attract much attention of researchers in the study of fluid mechanics. This thesis mainly focuses on the wave configuration of shock wave re-flection for the TSD (Transonic Small Disturbance) equations. This thesis discusses the Riemann problem for the TSD equations and specify the existence and the non-existence of the nonlinear wave configurations relating to the shock wave reflection, which gives a new explanation for the von Neumann paradox.Firstly, using geometric optics the author deduces that the Euler equations can approximate the UTSD (Unsteady Transonic Small Disturbance) equations in the introduction. Next, the author constructs the solution of the Riemann problem for the TSD equations under a certain condition by shock curves and centered simple wave curves and the author also shows that there exists no solution if the condition can not be satisfied. The details can be seen in Chapter1.Secondly, using shock curves and centered simple wave curves the author gives a condition under which the solution of the regular reflection for the TSD equations exists. The paper also proves that the regular reflection configuration is stable by solving a free boundary problem of the TSD equations. Next, the author proves that there exists no wave configuration of shock wave reflection for the TSD equations which consists of three shock waves by the shock jump conditions. In phase space, the paper proves that the TSD equations have a Mach configuration including a. centered simple wave and it does not have any shock wave reflection configuration which consists of four shock waves. Moreover, the author proves the stability of the Mach configuration including a centered simple wave by solving a free boundary problem of the TSD equations. The details can be seen in Chapter2to Chapter4.Finally, in the appendix, the author lists several lemmas which are used to prove the theorems. The details can be seen in Chapter5.