A Green's Function Approach to Wave Propagation and Potential Flow around Obstacles in Infinite Cylindrical Channels
Hans-Christof Stuwe, Peter Christian Werner · Mathematical Methods in the Applied Sciences · 1996
We study (a) acoustic waves generated by a time-harmonic force distribution and (b) the potential flow with prescribed velocity at infinity in an infinite cylinder Ω0 = Ω′×ℝ with bounded cross-section Ω′⊂ℝ2 in the presence of m embedded obstacles B1,…,Bm. By using Green's function Gκ(x,y) of the Neumann problem for the reduced wave equation ΔU+κ2U = 0 in the unperturbed domain Ω0, both problems can be reduced to integral equations over the boundaries of the obstacles. The main properties of Gκ(x,y), which are required for this approach, are derived in the first part of this paper.