Adaptive FEM for Analysis, Design, and Control of 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流动到制造过程。事实上，CFD预测现在构成了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，确定一个人可以分配给预测的置信度是很重要的。工程师在使用CFD时必须回答两个问题：(1)计算机模型能否产生准确的解决方案？以及(2)解决方案可靠吗？我们的研究将开发理论和工具来回答这两个问题。*自适应方法研究的第一轴将为自动控制CFD结果的精度提供一个框架。CFD的物理现实主义通常通过*将CFD预测与实验数据进行比较来评估。这项任务的困难在于预测和测量都受到不确定性的影响。对于实验来说，这是由于测量精度和数据处理技术所致。对于预测，有两个误差来源：离散化误差(通过自适应控制)和输入到CFD模型的数据中的不确定性(制造公差、操作条件等)。*我们不确定性分析研究的第二个轴将开发理论和技术，以产生CFD预测的量化不确定性估计。*应用程序第三轴将我们的研究应用于具有挑战性的工业相关问题，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确定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新方法上，以控制复杂流动的行为，而不是乏味和耗时的分析。我们建议的方法提供了极好的成功前景，因为它扩展了设计师工艺的范围，它构成了工程师和设计师使用的现有程序的自然和合乎逻辑的延伸。

Computational Fluid Dynamics (CFD) plays an increasingly important role in engineering. Its uses range from the analysis of the flow around an airplane to that 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 using CFD: (1) does the computer model yield accurate solutions? and (2) are the solutions reliable? Our research will develop 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.