Mathematical Foundations of Future Turbulent Flow Simulations

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The use of computational simulation methods is a requirement to address many challenging problems involving fluid flow. This is the case, for example, with regard to research focused on the improved use of wind energy, the optimization of aircraft flight, and the prediction of weather and climate. Basically all flows of practical relevance are turbulent. Despite intense research of more than fifty years, accurate and computationally feasible predictions of turbulent flows are still one of our biggest challenges. Over the last decades it became clear that significant progress is needed in particular in two directions. First, with respect to moderately turbulent flows, the development of simulation methods is needed that enable exact flow predictions. Second, with respect to highly turbulent flows, the development of hybrid simulation methods (which combine different simulation tools) is needed that enable optimal flow predictions. Unfortunately, currently existing simulation methods of these two types suffer from serious mathematical problems (computational instabilities, the lack of control). A detailed research plan for solving these problems combined with a carefully organized plan for demonstrating the benefits of new simulation methods are presented. The new computational simulation methods to be developed under this effort will enable, e.g., a much more efficient use of wind energy and optimization of aircraft flight. The project addresses one of the most pressing mathematical problems: the development of accurate and computationally feasible simulation methods for turbulent flows, which is highly relevant to a variety of technical problems. Research will be performed in two main directions. The track 1 direction is the development of dynamic Large Eddy Simulation (LES) methods that enable correct predictions of low and moderate Reynolds number flows. The track 2 direction is the development of hybrid methods involving LES and Reynolds-Averaged Navier-Stokes (RANS) equations. The use of such hybrid RANS-LES methods is the most promising way to optimally predict flows at high Reynolds numbers. The current development of track 1 and track 2 methods suffers from serious mathematical problems (the instability of dynamic LES, the lack of control of RANS and LES modes in hybrid RANS-LES, the determination of the degree of flow resolution of these methods). A detailed research plan for solving these problems and demonstrating the advantages of novel simulation methods will be pursued. The project will have significant broader impacts. The dissemination plan specifies the broad and efficient distribution of project results and codes to the community. In addition to the presentation of talks and journal papers, the basic project results will be posted on the main web page of the turbulence research community. The education plan specifies several educational impacts including the organization of a summer school on the use of stochastic methods in fluid dynamics for graduate students and faculty. Service to the society will be provided by bringing project results to the attention of NSF, NASA, and DOE, as well as other researchers pursuing questions in this field, to illustrate new opportunities to deal with relevant turbulent flow predictions.