Gasdynamic wave interaction in two spatial dimensions
S. R. SANDERSON a1p1 a1 Graduate Aeronautical Laboratories, California Institute of Technology, Pasadena, CA 91125, USA p1 Present address: GE Global Research, 1 Research Circle, Niskayuna, NY 12309, USA.
We examine the interaction of shock waves by studying solutions of the two-dimensional Euler equations about a point. The problem is reduced to linear form by considering local solutions that are constant along each ray and thereby exhibit no length scale at the intersection point. Closed-form solutions are obtained in a unified manner for standard gasdynamics problems including oblique shock waves, Prandtl–Meyer flow and Mach reflection. These canonical gas dynamical problems are shown to reduce to a series of geometrical transformations involving anisotropic coordinate stretching and rotation operations. An entropy condition and a requirement for geometric regularity of the intersection of the incident waves are used to eliminate spurious solutions. Consideration of the downstream boundary conditions leads to a formal determination of the allowable downstream matching criteria. By retaining the time-dependent terms, an approach is suggested for future investigation of the open problem of the stability of shock wave interactions.
(Received March 6 2003) (Revised November 20 2003)