Theoretical study of scattering problem with mixed boundary conditions. I - Mathematical aspect

Abstract

This paper provides a mathematical procedure to analyze an acoustic field scattered by a discontinuous surface of finite length submerged in a two-dimensional uniform flow. This classical is the boundary value problem including both Dirichlet and Neumann boundary conditions. The finite geometry, unlike the semi-infinite geometry, yields a three-part mixed boundary value resulting in strongly coupled integral equations. There are serious difficulties in dealing with those simultaneous integral equations, which have multi-valued functions as their Kernels. Accordingly, in this study, a more manageable integral equation is established in the presence of mean flow. The formulation is performed in the complex domain and is based on the Wiener-Hopf technique. Two uncoupled Fredholm integral equations are obtained by deriving the similarity of the kernel function, the interval of integration and the unknown functions. Morever, the solution procedure is introduced using the method of degenerate kernel and the complex line integral.