Influence of viscosity on the scattering of an air pressure wave by a rigid body: a regular boundary integral formulation

摘要

This paper gives a regular vector boundary integral equation for solving the problem ofnviscous scattering of a pressure wave by a rigid body. Firstly, single-layer viscousnpotentials and a generalized stress tensor are introduced. Correspondingly, generalizednviscous double-layer potentials are defined. By representing the scattered field as ancombination of a single-layer viscous potential and a generalized viscous double-layernpotential, the problem is reduced to the solution of a vectorial Fredholm integralnequation of the second kind. Generally, the vector integral equation is singular. However,nthere is a particular stress tensor, called pseudostress, which yields a regular integralnequation. In this case, the Fredholm alternative applies and permits a direct proof of thenexistence and uniqueness of the solution. The results presented here provide thenfoundation for a numerical solution procedure.