THE POINT-MATCHING METHOD ON DISSIPATIVE SILENCERS OF ARBITRARY CROSS-SECTION

Abstract

A most straightforward and simple numerical technique known as point-matching, or collocation, is used to obtain the wavenumbers and eigenmodes of an infinite cylindrical dissipative silencer of arbitrary cross-section in the case of negligible mean flow. This technique provides an alternative both to the different numerical variational formulations used in the literature so far, as well as to possible analytical techniques such as for instance the null-field approach. In principle the point-matching method does not suffer from any severe restrictions upon the cross-sectional shape of the silencer even though the rate of convergence is strongly related to the geometry. The grid used in the collocation is also found to be critical for the rate of convergence. Especially in the case of the points in the collocation separated by equal polar angles, the results are poor. To handle this complication a simple technique for choosing the grid is proposed. To show the applicability of the point-matching method, a commercial dissipative silencer is analyzed and comparisons with measurements are made.