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Fourier time spectral method for subsonic and transonic flows

Acta Mechanica Sinica 2016年第3期32卷 380-396页

作者： Lei Zhan Feng Liu dimitri papamoschou School of Aeronautics Northwestern Polytechnical UniversityXi'an 710072China Department of Mechanical and Aerospace Engineering University of CaliforniaIrvineCA 92697USA

The time accuracy of the exponentially accurate Fourier time spectral method（TSM） is examined and compared with a conventional 2nd-order backward difference formula（BDF） method for periodic unsteady flows. In particular, detailed error analysis based on numerical computations is performed on the accuracy of resolving the local pressure coefficient and global integrated force coefficients for smooth subsonic and non-smooth transonic flows with moving shock waves on a pitching airfoil. For smooth subsonic flows, the Fourier TSM method offers a significant accuracy advantage over the BDF method for the prediction of both the local pressure coefficient and integrated force coefficients. For transonic flows where the motion of the discontinuous shock wave contributes significant higherorder harmonic contents to the local pressure fluctuations,a sufficient number of modes must be included before the Fourier TSM provides an advantage over the BDF *** Fourier TSM, however, still offers better accuracy than the BDF method for integrated force coefficients even for transonic flows. A problem of non-symmetric solutions for symmetric periodic flows due to the use of odd numbers of intervals is uncovered and analyzed. A frequency-searching method is proposed for problems where the frequency is not known a priori. The method is tested on the vortex shedding problem of the flow over a circular cylinder.

关键词： Fourier time spectral method(TSM) Pitching airfoil Transonic flow Non-symmetric solution Computational efficiency Vortex shedding flow Frequency search

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