POD降阶算法中对基模态表达的改进

由一系列已知的相近流场解重新组合成一组正交分解(POD)的基模态。利用这些模态的线性组合构造绕一任意翼型的流场,使计算的未知量数目仅为所取相近解流场个数,而传统方法的未知量数目为网格单元数的4倍,因此极大地减少了未知量的数目,将其用于翼型优化,计算量会显著减少。给定的一系列相近流场解,是通过计算快照得到的,这些快照是形成正交模态的根本,直接影响近似计算的准确程度。本文提出了一种新的扰动方法,即通过扰动翼型的关键控制点反求翼型函数得到快照。通过几个已知的翼型解对子空间的投影比较可以看出,该方法的空间表达能力优于常用的加局部凸起的H icks-H enne函数的方法,而且近似计算的准确程度也更好。最后,探讨了正交分解的必要性,阐明利用POD降阶模型方法计算流场可以迅速收敛的内在原因。

Modification to Basic Modes of Reduced Order Model for Computing Airfoil Flow Field

A series of known approximate flow field solutions are reassembled into basic modes based on the proper orthogonal decomposition(POD).By using the arbitrary airfoil Euler solution with these modes,the number of unknowns is equal to the number of approximate flow field and the number of traditional CFD unknowns is equal to the quadruple of the mesh amount.Therefore,computational costs are greatly reduced especially in the field of aerodynamic shape optimization.The approximate flow field(snapshot) is obtained by computing a series of perturbed airfoils important to POD modes and will affect the computing result.This paper presents a new method-perturbing airfoil function to obtain the snapshots.The result is better than adding Hicks-Henne bump functions by the comparison of doing subspace projection.This paper also discusses the necessity of POD and describes the reason that one can obtain the approximate solution quickly with some least-square methods.