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 - http://www.scopus.com/inward/record.url?eid=2-s2.0-0025448909&partnerID=MN8TOARS
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 -