Development and Application of Advanced Sensitivity Equation Methods for Complex Flows

计算流体力学（CFD）在工程中发挥着越来越重要的作用。它的应用范围从分析飞机周围的气流到分析制造过程。事实上，CFD预测现在已经成为工程决策和科学发现的基础。因此，在已知物理系统和用来描述它的模型的情况下，确定人们可以赋予预测的置信度是很重要的。工程师在进行CFD分析时必须回答两个问题：计算机模型是否产生准确的解决方案？解决方案可靠吗？我们的研究将为回答这两个问题提供理论和工具。自适应方法研究的第一轴将为CFD结果的自动化精度控制提供一个框架。通常通过比较CFD预测和实验数据来评估CFD的物理真实感。这项任务的困难在于预测和测量都受到不确定性的影响。对于实验，这是由于测量精度和数据处理技术。对于预测，有两个误差来源：离散误差（通过自适应控制）和CFD模型输入数据中的不确定性（制造公差，操作条件等）。我们研究不确定性分析的第二个轴将发展理论和技术，以产生CFD预测的量化不确定性估计。第三个应用轴将我们的研究应用于工业相关的挑战性问题，以展示我们方法的范围和广度，我们研究的原创性及其影响。最后，我们的研究将为工程分析和设计提供新的工具。它们将使工程师能够识别控制流动响应的关键参数，从而使他们能够将精力集中在创新设计和控制复杂流动行为的新方法上，而不是在繁琐和耗时的分析上。我们提出的方法提供了很好的成功前景，因为它扩展了设计师工艺的范围，并且构成了工程师和设计师使用的现有程序的自然和逻辑扩展。

Computational Fluid Dynamics (CFD) plays an increasingly important role in engineering. Its uses range from the analysis of the flow around an airplane to the analysis of manufacturing processes. In fact, CFD predictions now form the basis of engineering decisions and of scientific discovery. Thus, it is important to determine the level of confidence one can assign to a prediction given what is known about the physical system and the model used to describe it. Engineers must answer two questions when performing CFD analyses: does the computer model yield accurate solutions? and are the solutions reliable? Our research will provide theories and tools to answer these two questions. A FIRST axis of research on ADAPTIVE METHODS will provide a framework for automating accuracy control of CFD results. Physical realism of a CFD is usually assessed by comparing CFD predictions to experimental data. The difficulty in this task lies in the fact that both predictions and measurements suffer from uncertainty. For experiments, this is due to measurement accuracy and data processing techniques. For predictions, there are two sources of errors: discretization errors (controlled through adaptivity) and uncertainties in the data input to the CFD model (manufacturing tolerances, operating conditions, etc.). A SECOND axis of our research on UNCERTAINTY ANALYSIS will develop theory and techniques to produce quantified uncertainty estimates of the CFD predictions. A third AXIS on APPLICATIONS applies our research to challenging problems of industrial relevance to demonstrate the scope and breadth of our approach , the originality of our research and its impact. Finally, our research will yield new tools for engineering analysis and design. They will allow engineers to identify key parameters controlling the flow response, thus allowing them to focus their efforts on innovative designs and new approaches to control the behavior of complex flows rather than on tedious and time consuming analysis. Our proposed approach offers excellent perspective of success because it extends the reach of the designer craft and it constitutes a natural and logical extension of existing procedures used by engineers and designers.