应用傅里叶时间谱方法求解二维跨音速流动问题解的精度研究  

Study on Accuracy of the Solutions Using the Fourier Time Spectral Method for Two-dimensional Transonic Flows

作　　者：詹磊[1] 刘锋[1,2] 

机构地区：[1]西北工业大学航空学院,西安710072 [2]加州大学尔湾分校机械与航空工程系,美国ca926973975

出　　处：《航空工程进展》2015年第4期395-404,共10页Advances in Aeronautical Science and Engineering

摘　　要：为了从时间离散精度的角度评估傅里叶时间谱方法的实际计算效率,对用该方法求解二维跨音速流动问题的解进行了精度研究。通过求解Euler方程模拟俯仰振动NACA0012翼型的周期性非定常流动。结果表明:傅里叶时间谱方法可以使用很大的时间间隔较为准确地模拟有激波存在的周期性跨音速流动;对于此类流动问题,相比二阶向后差分公式法,傅里叶时间谱方法在预测翼型表面压力系数积分量特别是升力系数的时间变化规律方面具有明显的计算效率优势;用于模拟翼型表面压力系数自身的时间变化规律时,傅里叶时间谱方法具有不低于二阶向后差分公式法的计算效率。To evaluate the actual computational efficiency of the Fourier time spectral method（TSM）in the aspect of the time-discretization accuracy,the accuracy analysis is performed on the computational solutions of two-dimensional transonic flows.The periodic flows over a pitching NACA0012 airfoil are simulated by solving unsteady Euler equations.Results show that large time interval could be used for the Fourier TSM to simulate periodic transonic flows even when shock waves occur.Error analysis shows that,compared to the 2nd order backward difference formula（BDF）method,the Fourier TSM is much more efficient in predicting the temporal variation of quantities that are integrated from the surface pressure coefficient,especially the lift coefficient.When predicting the temporal variation of the surface pressure coefficient,the computational efficiency of the Fourier TSM is not lower than that of the 2nd order BDF method.

关 键 词：跨音速流动 傅里叶时间谱方法 激波运动 计算效率 

分 类 号：V211.3[航空宇航科学与技术—航空宇航推进理论与工程]