Visiting Researcher: BiGlobal Methods for Optimal Flow Perturbations

自20世纪80年代中期以来，计算流体动力学在粘性、非定常和分离流中的研究应用主要集中在直接模拟与时间相关的Navier-Stokes方程。在这段时间里，计算能力的提高和计算方法的进步使得可以进行更大规模的模拟，随之而来的是更大量的数据。然而，分析人员仍然面临的主要问题之一，特别是在处理非定常和过渡/湍流模拟时，是如何吸收、分析和应用这些大量数据的问题。开发复杂的几何稳定性（bigliterature）和分叉分析来理解潜在的基本状态的主导不稳定模式提供了一个强有力的工具来应用计算分析来补充实验数据。尽管bigliterature稳定性方法在复杂几何形状的各种应用中取得了成功，例如海崖体流动，但这种经典方法仍然有一些重大的失败，例如，发现管状Poiffille流和平面Couette流都是渐近线性稳定的（而众所周知，它们都支持湍流）。最近，人们普遍认识到线性不稳定模式和技术的非正态性的基本重要性，使用伴随方法来确定最佳的流动扰动。然而，已发表的关于正则模态和伴随模态的应用的著作，几乎无一例外地都是处理一维或准一维边界层型流动，而大涡稳定性分析只处理正则模态的渐近不稳定性。在本提案中，我们寻求开始的过程中，通过扩展我们现有的高精度的光谱/$hp$元素稳定性分析的渐近不稳定性的最优增长的问题，但在一般的geometrics.The研究人员认为，显着的进一步进展将只可能通过继续直接合作。通过电子邮件交流可以进行一定数量的有用交流和渐进式进步，但对于快速进步和重大进步来说，这不能取代面对面的互动。因此，本申请寻求资金，以允许布莱克本博士在2006年对英国进行外部访问。在这次访问期间，布莱克本，舍温和巴克利将建立在现有的研究和巩固进一步的工作，将在干预期间进行。

Research applications of computational fluid dynamics in viscous, unsteady and separated flows since the mid-1980s largely focused on direct simulation of the time-dependent Navier--Stokes equations. Increases in computational power and advances in computational methods over this time have permitted significantly larger simulations to be performed, with concomitantly larger volumes of data as the outcome. However one of the major issues still facing the analyst, particularly when dealing with unsteady and transitional/turbulent simulations, is the question of how to assimilate, analyse and apply this great wealth of data. The development complex geometry stability (biglobal) and bifurcation analyses to understand the dominant instability modes of the underlying basic state have provided a powerful tools to applying computational analysis which complement experimental data.Despite the successes of biglobal stability methods in complex geometries in various application such as bluff body flows there have still been a number significant failures of this classical approach, e.g. the finding that both tubular Poiseuille flow and planar Couette flow are asymptotically linearly stable (whereas they are both well-known to support turbulence). More recently, there has been a general recognition of the fundamental importance of non-normality of linear instability modes and techniques using adjoint methods to determine optimal flow perturbations. However the published works dealing with applications of regular and adjoint modes have almost without exception dealt with either one-dimensional or quasi-one-dimensional boundary-layer type flows, while biglobal stability analyses have dealt only with with the asymptotic instability of regular modes. In the present proposal, we seek to begin the process of marrying the methods, by extending our existing highly accurate spectral/$hp$ element stability analysis for asymptotic instabilities to the problem of optimal growth, but in general geometries.The researchers believe significant further progress will only be possible through continued direct collaboration. A certain amount of useful interchange and incremental advance can take place through email exchanges, but for rapid progress and significant advances this cannot replace face-to-face interaction. This application therefore seeks funding to allow an external visit to the UK by Dr~Blackburn in 2006. During this visit Blackburn, Sherwin and Barkley will build on existing research and consolidate further work which will be undertaken in the intervening period.