Free boundary problems for the unsteady transonic small disturbance equation: Transonic regular reflection
Using a free boundary problem approach, the authors formulate and solve a transonic regular reflection problem for unsteady transonic small disturbance equation. The method applies to self-similar shock reflection when the incident shock angle is large enough to permit a regular reflection configuration with a subsonic state behind the reflected shock. The main result is the existence theorem for nonuniform subsonic flow behind the reflected schok. The flow velocity satisfies a quasilinear elliptic equation which is coupled to Rankine-Hugoniot equations for reflected shock, forming a free boundary problem on a part of the boundary. Because the equation is not uniformly elliptic in the entire domain, a cut off is introduced to give a bounded domain, together with cut offs for the coefficients.
unsteady transonic small disturbance equation
scientific article; zbMATH DE number 1757304