A viscous-acoustic boundary element formulation based on analytical-numerical matching

Abstract

Analytical-numerical matching (ANM) is an analysis scheme that combines a low-resolution global numerical solution with a high-resolution local analytical solution and a matching solution to form a uniformly valid composite solution. The application of ANM to harmonically oscillating bodies in a fluid leads to a novel reformulation of boundary element problems in acoustics and aeroacoustics. The singular kernal encountered in the integral equation is handled simply within the analytical local solution. The numerical implementation utilizes a smoothed Green’s function solution to the governing equation with a distributed source term. Because the singular behavior has been removed from the numerical aspect of the problem, the approach converges rapidly and exhibits insensitivity to node (control point) location. The method allows low-resolution numerics to be combined with analytical corrections to obtain high accuracy solutions using a robust calculation scheme. The method has recently been extended to include viscous effects within the local solution. The appropriately modified global solution remains irrotational and can be expressed in terms of a smoothed potential. Sample results are shown for radiation from plates up to high frequencies. Ongoing research on ANM BEM is described, including work to include nonlinear convection within the viscous flow effects.