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

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。

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

To evaluate the actual computational efficiency of the Fourier Time Spectral Method in the aspect of the time-discretization accuracy, accuracy analysis is performed on the computational solutions of two-dimensional transonic flows. Computational results of periodic flows over a pitching NACA0012 airfoil by solving unsteady Euler equations show that large time interval could be used for the Fourier TSM to model 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.