Characteristic decompositions and interactions of rarefaction waves of 2-D Euler equations

This paper is concerned with classical solutions to the interaction of two arbitrary planar rarefaction waves for the self-similar Euler equations in two space dimensions. We develop the direct approach, started in Chen and Zheng (in press) [3], to the problem to recover all the properties of the solutions obtained via the hodograph transformation of Li and Zheng (2009) [14]. The direct approach, as opposed to the hodograph transformation, is straightforward and avoids the common difficulties of the hodograph transformation associated with simple waves and boundaries. The approach is made up of various characteristic decompositions of the self-similar Euler equations for the speed of sound and inclination angles of characteristics.