Investigation of the Flow Singularity at the Triple Point of Stationary Irregular Mach Reflection of a Shock Wave in a Plane Channel

Abstract

The problem of stationary Mach reflection of a Shockwave in a plane channel is considered within the framework of the Euler model. Emphasis is placed on an investigation of the flow parameters at the triple point. In an analytical investigation the local theory for curvilinear shock waves is employed. The conditions on the input data of the problem, at which singularity is realized at the triple point, are derived. Under the singularity conditions the flow parameter gradients and the curvatures of the shock fronts and tangential discontinuity at the triple point increase without bound. In the numerical investigation the second-order Godunov method is used, together with a new technology of contracting the grid toward the triple point in combination with the discontinuity fitting. The calculations confirm the theoretically predicted singularity boundary. Additional numerical experiments show that the singularity boundary is conserved, when artificial source terms are introduced into the energy equation. These results allow one to put forward the hypothesis that the singularity within the same boundaries is also realized for other two-dimensional flows with irregular shock-wave reflection.