Quantification of Numerical Damping in the Acoustic Boundary Element Method for Two-Dimensional Duct Problems

Abstract

Spurious numerical damping in the collocation boundary element method is considered for plane sound waves in two-dimensional ducts subjected to rigid and absorbing boundary conditions. Its extent is quantified in both conditions based on a damping model with exponential decay, and meshes of linear and quadratic continuous elements are studied. An exponential increase of numerical damping with respect to frequency is found and the results suggest an upper bound for given element-to-wavelength ratios. The quantification of numerical damping is required for evaluation of meshes covering a large number of waves, and real damping phenomena can be prevented from overestimation.