Adaptive FEM for Analysis, Design, and Control of Complex Flows

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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.