Stabilization of linear flow solver for turbomachinery aeroelasticity using Recursive Projection method
Stabilization of linear flow solver for turbomachinery aeroelasticity using Recursive Projection method
复制标题
使用递归投影法稳定涡轮机械气动弹性线性流动求解器
DOI：
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发表时间：
2004
期刊：
影响因子：
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通讯作者：
M. Giles
中科院分区：
文献类型：
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作者：
M. Campobasso;M. Giles
涡轮机械气动弹性的线性分析依赖于小水平非定常的假设，并且需要求解非线性稳态和线性非定常流动方程。分析的目的是计算复杂的流动解，该解表示感兴趣的不稳定频率的不稳定流动扰动的幅度和相位。 HYDRA 代码套件的线性谐波欧拉/纳维斯托克斯求解器的求解过程由预条件定点迭代组成，在某些情况下会变得数值不稳定。之前的工作已经强调了这些数值不稳定性的物理根源，并证明了通过使用广义最小残差（GMRES）求解器包装线性代码的核心部分来实现代码稳定性。总结了另一种算法（即递归投影法）的实现和使用。该求解器被证明非常适合在没有数值不稳定的情况下稳定定点迭代并提高其收敛速度。在涡轮机械气动弹性线性分析的框架中，该方法在计算上可以与 GMRES 方法竞争。
The linear analysis of turbomachinery aeroelasticity relies on the assumption of small level of unsteadiness and requires the solution of both the nonlinear steady and the linear unsteady flow equations. The objective of the analysis is to compute a complex flow solution that represents the amplitude and phase of the unsteady flow perturbation for the frequency of unsteadiness of interest. The solution procedure of the linear harmonic Euler/Navier‐Stokes solver of the HYDRA suite of codes consists of a preconditioned fixed-point iteration, which in some circumstances becomes numerically unstable. Previous work had already highlighted the physical origin of these numerical instabilities and demonstrated the code stabilization achieved by wrapping the core part of the linear code with a Generalized Minimal Residual (GMRES) solver. The implementation and the use of an alternative algorithm, namely, the Recursive Projection Method, is summarized. This solver is shown to be well suited for both stabilizing the fixed-point iteration and improving its convergence rate in the absence of numerical instabilities. In the framework of the linear analysis of turbomachinery aeroelasticity, this method can be computationally competitive with the GMRES approach.