An efficient, direct finite difference method for computing sound propagation in arbitrarily shaped twodimensional and axisymmetric ducts without flow
Abstract
An efficient, direct finite difference method is presented for computing sound propagation in nonstepped twodimensional and axisymmetric ducts of arbitrarily varying cross section without mean flow. The method is not restricted by axial variation of acoustic impedance of the duct wall linings. The nonuniform twodimensional or axisymmetric duct is conformally mapped numerically into a rectangular or cylindrical computational domain using a new procedure based on a method of fast direct solution of the CauchyRiemann equations. The resulting Helmholtz equation in the computational domain is separable. The solution to the governing equation and boundary conditions is expressed as a linear combination of fundamental solutions. The fundamental solutions are computed only once for each duct shape by means of the fast direct cyclic reduction method for the discrete solution of separable elliptic equations. Numerical results for several examples are presented to show the applicability and efficiency of the method.
 Publication:

AIAA, Aerospace Sciences Meeting
 Pub Date:
 February 1978
 Bibcode:
 1978aiaa.meetQ....C
 Keywords:

 Acoustic Ducts;
 Ducted Flow;
 Finite Difference Theory;
 Run Time (Computers);
 Sound Propagation;
 Acoustic Impedance;
 Acoustic Propagation;
 Axisymmetric Flow;
 Boundary Conditions;
 Boundary Value Problems;
 CauchyRiemann Equations;
 Conformal Mapping;
 Elliptic Differential Equations;
 Helmholtz Equations;
 Two Dimensional Flow;
 Acoustics