An efficient, direct finite difference method for computing sound propagation in arbitrarily shaped two-dimensional and axisymmetric ducts without flowAn efficient, direct finite difference method is presented for computing sound propagation in non-stepped two-dimensional 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 non-uniform two-dimensional 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 Cauchy-Riemann 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.
Document ID
19780040117
Acquisition Source
Legacy CDMS
Document Type
Conference Paper
Authors
Chakravarthy, S. (Iowa State University of Science and Technology, Ames, Iowa, United States)
Date Acquired
August 9, 2013
Publication Date
February 1, 1978
Subject Category
Acoustics
Report/Patent Number
AIAA PAPER 78-332
Meeting Information
Meeting: Annual Meeting and Technical Display
Location: Washington, DC
Start Date: February 7, 1978
End Date: February 9, 1978
Sponsors: American Institute of Aeronautics and Astronautics