时频域混合方法在非定常流计算中的对比研究

Comparison of Hybrid Time and Frequency Domain Methods for Analyzing Unsteady Flows

时频域混合方法包括时域谐波平衡(HB)方法和非线性频域(NLFD)方法。两种方法都是通过谱方法离散时间偏导数项,从而将非定常控制方程转化为准定常控制方程进行求解。不同的是,前者求解不同时刻的时域控制方程,求解变量是不同时刻的流场变量;而后者通过同时对流场变量及方程残差做傅里叶变换求解不同频率组分的频域控制方程,求解的是流场变量的傅里叶系数。除了算法上的差距,目前关于这两种时频域混合方法的优缺点知之甚少,国内外对比研究这两种方法的文献也未发现,这增加了研究人员选择合适时频域降阶方法进行非定常流场分析时的困难。本文将分别采用理论分析及数值验证的方式详细对比研究这两种方法的优缺点,为研究人员在选择这两种降阶方法的时候提供借鉴。

Hybrid time and frequency domain methods include the time domain harmonic balance method(HB)and the nonlinear frequency domain method(NLFD).Both methods make use of spectral method to discretize the time derivative term to transfer the unsteady governing equations into quasi-steady governing equations.The difference lies in that the former solves the time domain unsteady flow governing equations at different time instants for the flow variables at different time instants,however the latter solves the frequency domain governing equations for the Fourier coefficients of flow variables by simultaneously performing Fourier transform on both flow variables and residuals.Apart from the difference in algorithms,at present the pros and cons about the two methods are unclear,and little can be found in the open literature about the comparison of the two methods.This increases the difficulty in selecting an appropriate method for the analysis of unsteady flows.This paper will utilize both theoretical analysis and numerical analysis to make a comparison between the two methods,and provide guidelines for researchers to make a choice.