Corner Conditions for Weak Shock Diffraction by a Wedge

Abstract

In deriving the first-order approximate solutions to the problem of the diffraction of a propagating pressure discontinuity by a rigid wedge in a non-viscous, non-thermally conducting, polytropic gas, Miles (1952) and Friedlander (1958) have taken as the comer conditions that the pressure remains finite and that the velocity may have an integrable singularity, whereas Keller and Blank (1951) gave no discussion of the comer conditions at all. Friedlander imposed the above-mentioned conditions in order to ensure the validity of the uniqueness theorem of the initial value problem for the wave equation, whereas Miles invoked them through physical requirements but gave no details.