谐波平衡法在非定常流场中的应用

谐波平衡法（HBM）适用于模拟周期性非定常流场。求解这类问题时，只需要一个周期中几个等距时刻的流场解，即可重建整个周期流动的时间历程，计算效率较高；同时还采用谱算子精确求解流场变量对物理时间的导数项，保障了算法的计算精度。鉴于此，详细介绍了谐波平衡法的原理和实现过程，并给出了如何在现有计算程序下实现谐波平衡法的流程。取跨声速翼型和超声速钝锥两个周期性强迫俯仰振荡绕流为例，以双时间步方法为参考，对谐波平衡法的效率和精度作了详细的考核和分析。计算结果表明，谐波平衡法的内存消耗较大，谐波数N_H=2时约为双时间步方法的4倍，但谐波平衡法取得与双时间步方法相近结果的计算时间仅为后者的1/5。因此，谐波平衡法是一种有应用前景的工程实用方法。对于长周期问题，谐波平衡法的优势更加明显。

Application of Harmonic Balance Method to Unsteady Flow Field

The harmonic balance method (HBM) is adapted in this paper to solve periodic unsteady flow problems. For these problems, this method has a high computational efficiency because it can rebuild the time history of a complete periodic flow with only computations at several equally spaced time intervals. The order of accuracy of the algorithm is guaranteed by employing a spectral operator to accurately solve the derivatives of the flow variables against the physical time. The mechanism and realization of the harmonic balance method are introduced in detail, and the process of modifying the existing code is presented. Two periodically forced pitching oscillation test cases are used to demonstrate the efficiency and accuracy of the harmonic balance method, including an airfoil in subsonic flow and a bluntcone configuration in hypersonic flow.A comparison is made with the dual time stepping method, and the results show that the harmonic balance method requires considerably more CPU memory, with the memory in N_H=2 case being four times that of the dual time-stepping method. Yet it can reduce the computing time greatly with only about 1/5 in N_H=2 case of that needed by the dual time-stepping method to obtain similar results. Therefore the harmonic balance method is an engineeringly applicable method with bright prospects. For problems with a long period, it has a more obvious advantage.