Spectral simulations of an unsteady compressible flow past a circular cylinder

Wai-Sun Don; David Gottlieb

doi:10.1016/0045-7825(90)90013-C

Spectral simulations of an unsteady compressible flow past a circular cylinder

Wai-Sun Don^*
, David Gottlieb

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

22 Citations (Scopus)

Abstract

An unsteady compressible viscous wake flow past a circular cylinder has been successfully simulated using spectral methods. A new approach in using the Chebyshev collocation method for a periodic problem is introduced. We have further proved that the eigenvalues associated with the differentiation matrix are purely imaginary, reflecting the periodicity of the problem. It has been shown that the solution of a model problem has exponential growth in time if an ‘improper’ boundary conditions procedure is used. A characteristic boundary conditions, which is based on the characteristics of the Euler equations of gas dynamics, has been derived for the spectral code. The primary vortex shedding frequency computed agrees well with the results in the literature for Mach = 0.4, Re = 80. No secondary frequency is observed in the power spectrum analysis of the pressure data.

Original language	English
Pages (from-to)	39-58
Number of pages	20
Journal	Computer Methods in Applied Mechanics and Engineering
Volume	80
Issue number	1-3
DOIs	https://doi.org/10.1016/0045-7825(90)90013-C
Publication status	Published - Jun 1990

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title = "Spectral simulations of an unsteady compressible flow past a circular cylinder",

abstract = "An unsteady compressible viscous wake flow past a circular cylinder has been successfully simulated using spectral methods. A new approach in using the Chebyshev collocation method for a periodic problem is introduced. We have further proved that the eigenvalues associated with the differentiation matrix are purely imaginary, reflecting the periodicity of the problem. It has been shown that the solution of a model problem has exponential growth in time if an {\textquoteleft}improper{\textquoteright} boundary conditions procedure is used. A characteristic boundary conditions, which is based on the characteristics of the Euler equations of gas dynamics, has been derived for the spectral code. The primary vortex shedding frequency computed agrees well with the results in the literature for Mach = 0.4, Re = 80. No secondary frequency is observed in the power spectrum analysis of the pressure data.",

author = "Wai-Sun Don and David Gottlieb",

note = "Publisher Copyright: {\textcopyright} 1990. Funding Information: The research reported here is part of the first author{\textquoteright}s thesis supported by NASA Langley{\textquoteright}s Graduate Program in Aeronautics (Grant NAG-1-703). The second author was supported in part by the U.S. Air Force of Scientific Research under grant AF-85-030 and by NSF grant DMS-8810150.",

year = "1990",

month = jun,

doi = "10.1016/0045-7825(90)90013-C",

language = "English",

volume = "80",

pages = "39--58",

journal = "Computer Methods in Applied Mechanics and Engineering",

issn = "0374-2830",

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number = "1-3",

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TY - JOUR

T1 - Spectral simulations of an unsteady compressible flow past a circular cylinder

AU - Don, Wai-Sun

AU - Gottlieb, David

N1 - Publisher Copyright: © 1990. Funding Information: The research reported here is part of the first author’s thesis supported by NASA Langley’s Graduate Program in Aeronautics (Grant NAG-1-703). The second author was supported in part by the U.S. Air Force of Scientific Research under grant AF-85-030 and by NSF grant DMS-8810150.

PY - 1990/6

Y1 - 1990/6

N2 - An unsteady compressible viscous wake flow past a circular cylinder has been successfully simulated using spectral methods. A new approach in using the Chebyshev collocation method for a periodic problem is introduced. We have further proved that the eigenvalues associated with the differentiation matrix are purely imaginary, reflecting the periodicity of the problem. It has been shown that the solution of a model problem has exponential growth in time if an ‘improper’ boundary conditions procedure is used. A characteristic boundary conditions, which is based on the characteristics of the Euler equations of gas dynamics, has been derived for the spectral code. The primary vortex shedding frequency computed agrees well with the results in the literature for Mach = 0.4, Re = 80. No secondary frequency is observed in the power spectrum analysis of the pressure data.

AB - An unsteady compressible viscous wake flow past a circular cylinder has been successfully simulated using spectral methods. A new approach in using the Chebyshev collocation method for a periodic problem is introduced. We have further proved that the eigenvalues associated with the differentiation matrix are purely imaginary, reflecting the periodicity of the problem. It has been shown that the solution of a model problem has exponential growth in time if an ‘improper’ boundary conditions procedure is used. A characteristic boundary conditions, which is based on the characteristics of the Euler equations of gas dynamics, has been derived for the spectral code. The primary vortex shedding frequency computed agrees well with the results in the literature for Mach = 0.4, Re = 80. No secondary frequency is observed in the power spectrum analysis of the pressure data.

UR - https://www.scopus.com/pages/publications/0025448909

U2 - 10.1016/0045-7825(90)90013-C

DO - 10.1016/0045-7825(90)90013-C

M3 - Journal article

SN - 0374-2830

VL - 80

SP - 39

EP - 58

JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

IS - 1-3

ER -

Spectral simulations of an unsteady compressible flow past a circular cylinder

Abstract

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