A finite element method for computing sound propagation in ducts

Abstract

In this paper, solutions of the equations which describe sound propagation in nonuniform ducts are computed with a finite element approach. A least squares approach is considered and compared to a Galerkin approach. The least squares problem is solved using an iterative method and compared with results obtained using direct Gaussian elimination. The accuracy of linear basis functions on triangles, bilinear basis functions on rectangles, and biquadratic basis functions on rectangles are compared. For the nonuniform ducts, the use of quadrilaterals as elements and an isoparametric map are considered. The biquadratics permit good approximation of curved boundaries and better convergence than the bilinear basis functions. Consequently, the finite element solution space consists of piecewise biquadratics defined on the finite element discretization of the geometry of the duct. Acoustic fields within uniform ducts both with and without flow have been computed and compare well with modal solutions and finite difference solutions. For nonuniform ducts without flow, the computed acoustic fields also compare well with exact or other computed solutions.