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A compact solution to computational acousticsThis paper demonstrates that the linearized, dimensional Euler equations for acoustic computation can be accurately solved as a set of decoupled first-order wave equations, and that if ordered properly, this system of simple waves has unambiguous, easily implemented boundary conditions, allowing waves of same group speeds to pass through numerical boundaries or comply with wall conditions. Thus, the task of designing a complex multi-dimensional scheme with approximate far-field boundary conditions reduces to the design of higher order schemes for the one-dimensional simple wave equation. A compact finite-difference scheme and a characteristically exact but numerically n(th) order accurate boundary condition are introduced for solving the first order wave equation. Spanning a three-point two-level stencil, this low-dispersion implicit scheme has a third order spatial accuracy when used on nonuniform meshes, fourth order accurate on uniform meshes, and a temporal accuracy of second order due to the choice of trapezoidal integration for algorithmic simplicity. The robustness and accuracy of the scheme are demonstrated through a series of numerical experiments and comparisons with published results. When tested on the one-dimensional wave equation on a uniform grid, this scheme allows a Gaussian wave packet to pass through any finite domain with low numerical dispersion characteristic of a spatially fourth-order scheme and reflections at numerical boundaries maintained below truncation error. On highly stretched and irregular grids, only mild dispersions are found in the solution while solutions by other methods fail or are severely distorted. Yet, this scheme is no more sophisticated to solve or implement than the Crank-Nicolson scheme. This scheme has been tested on four categories of the ICASE/LaRC benchmark problems, which include propagation of acoustic and convective waves in Cartesian and cylindrical domains, reflection of acoustic wave at stationary/moving boundaries, and sound generation by gust-blade interaction.
Document ID
19950023717
Acquisition Source
Legacy CDMS
Document Type
Conference Paper
Authors
Fung, K.-Y.
(Miami Univ. Coral Gables, FL., United States)
Man, Raymond S. O.
(Arizona Univ. Tucson, AZ., United States)
Davis, Sanford
(NASA Ames Research Center Moffett Field, CA, United States)
Date Acquired
September 6, 2013
Publication Date
May 1, 1995
Publication Information
Publication: NASA. Langley Research Center, ICASE(LaRC Workshop on Benchmark Problems in Computational Aeroacoustics (CAA) p 59-72 (SEE N95-30133 10-71)
Subject Category
Acoustics
Accession Number
95N30138
Funding Number(s)
CONTRACT_GRANT: NCA2-707
Distribution Limits
Public
Copyright
Work of the US Gov. Public Use Permitted.

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