Fourier time spectral method for subsonic and transonic flows

作     者：Lei Zhan Feng Liu Dimitri Papamoschou 

作者机构：School of AeronauticsNorthwestern Polytechnical UniversityXi'an 710072China Department of Mechanical and Aerospace EngineeringUniversity of CaliforniaIrvineCA 92697USA 

出 版 物：《Acta Mechanica Sinica》 (力学学报（英文版）)

年 卷 期：2016年第32卷第3期

页      面：380-396页

核心收录：

学科分类：080704[工学-流体机械及工程] 080103[工学-流体力学] 08[工学] 0807[工学-动力工程及工程热物理] 0802[工学-机械工程] 0701[理学-数学] 0801[工学-力学（可授工学、理学学位）] 0702[理学-物理学] 

基　　金：supported by the State Scholarship Fund of the China Scholarship Council (Grant 2009629129) 

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

摘      要：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.