Configuration And Numerical Simulation Of Shock Reflection For Potential Flow Equation

Euler equations can be used to describe the motion of perfect compressible fluid.In this thesis,we take two-dimensional isentropic Euler equations as an example to study a very important phenomenon in aerodynamics: shock reflection.When a plane shock hits an obstacle,it experiences a reflection process.Many physical experiments show that the patterns of shock reflection is very complex,which is determined by shock intensity and obstacle shape,etc.At present,the rigorous mathematical theory about shock reflection phenomenon is lack.In this thesis,we deduce the requirements of shock intensity and wedge angle when regular reflection occurs,and give the corresponding numerical simulation.The main works are as follow.In the first chapter,we introduce the physical background of shock reflection.In the second chapter,we consider the two-dimensional isentropic Euler equations for polytropic gas.First,we introduce the potential flow equation and solve the RankineHugoniot condition and the physical entropy condition of the two-dimensional Euler equations for isentropic fluids.The initial boundary value problem and the initial state of the incident shock in self-similar coordinates are further solved.Finally,We show that there are two configurations of shock regular reflection: supersonic and subsonic shock regular reflection.In the third chapter,we consider the local theory of shock reflection.The sufficient condition for shock regular reflection is that,when the shock hits a wedge,it produces a reflected shock and the corresponding post-shock constant state.In this chapter,when shock regular reflection occurs,the conditions of shock intensity and wedge angle are deduced.In the fourth chapter,we provide the numerical simulation of the conditions of shock intensity and wedge angle when shock regular reflection occurs using Matlab.