0
RESEARCH PAPERS

Finite Difference Time Marching in the Frequency Domain: A Parabolic Formulation for the Convective Wave Equation

[+] Author and Article Information
K. J. Baumeister

Lewis Research Center, National Aeronautics and Space Administration, Cleveland, OH 44135

K. L. Kreider

Department of Mathematical Sciences, The University of Akron, Akron, OH 44325-4002

J. Vib. Acoust 118(4), 622-629 (Oct 01, 1996) (8 pages) doi:10.1115/1.2888344 History: Received February 01, 1995; Revised July 01, 1995; Online February 26, 2008

Abstract

An explicit finite difference iteration scheme is developed to study harmonic sound propagation in ducts. To reduce storage requirements for large 3D problems, the time dependent potential form of the acoustic wave equation is used. To insure that the finite difference scheme is both explicit and stable, time is introduced into the Fourier transformed (steady-state) acoustic potential field as a parameter. Under a suitable transformation, the time dependent governing equation in frequency space is simplified to yield a parabolic partial differential equation, which is then marched through time to attain the steady-state solution. The input to the system is the amplitude of an incident harmonic sound source entering a quiescent duct at the input boundary, with standard impedance boundary conditions on the duct walls and duct exit. The introduction of the time parameter eliminates the large matrix storage requirements normally associated with frequency domain solutions, and time marching attains the steady-state quickly enough to make the method favorable when compared to frequency domain methods. For validation, this transient-frequency domain method is applied to sound propagation in a 2D hard wall duct with plug flow.

Copyright © 1996 by The American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.

References

Figures

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In