The two-dimensional unsteady supersonic flow around a convex corner

The flow around a convex corner is one of the most important elementary flows. In this paper, we are concerned with the two-dimensional (2D) unsteady supersonic flow turning a convex corner. We firstly give the properties of general centered simple for the two-dimensional isentropic irrotational pesudo-steady Euler equations. Then, by using the properties of general centered simple waves, we construct the self-similar solution for the two-dimensional isentropic irrotational supersonic flow around a convex corner and prove that the supersonic flow turns the convex corner by a centered expansion wave or a centered compression wave under appropriate conditions on the downstream state.