Simple waves for two-dimensional compressible pseudo-steady Euler system

A simple wave is defined as a flow in a region whose image is a curve in the phase space. It is well known that "the theory of simple waves is fundamental in building up the solutions of flow problems out of elementary flow pattern" see Courant and Friedrichs's chassical book "Supersonic Flow and Shock Waves". This paper mainly concerned with the geometric construction of simple waves for the 2D pseudo-steady compressible Euler system. Based on the geometric interpretation, the expansion or compression simple wave flow construction around a pseudo-stream line with a bend part are constructed. It is a building block that appears in the global solution to four contact discontinuities Riemann problems.