Numerical Analysis, Analysis and Modeling of Fluid Motion

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The accurate, efficient and reliable prediction of quantities in turbulent flows (the focus of the proposed research) forces systematic and integrated confrontation of basic issues in the modeling, analysis, numerical analysis and computation of turbulent flows, many of which are linked to basic issues in other flow problems and other areas of mathematics. Interconnected research sub-projects include: (i) Eduction of large coherent vortices and detection of false vortices created by models or numerics, (ii) Development and numerical analysis of high accuracy and efficiently solvable regularizations of fluid flow equations, (iii) New algorithms for ill-posed problems and applications, (iv) Development of LES models for compressible turbulence and analysis of their acoustic noise predictions, (v) Mathematical foundation for time-averaged large eddy simulation: continuous transitioning between direct numerical simulation, large eddy simulation and Reynolds averaged turbulence models, (vi) Uncoupling multi-physics fluid flow problems in fluid-structure interaction, groundwater-surface water models and fluid-fluid problems motivated by atmosphere-ocean coupling, and (v) Precise numerical analysis of time relaxation regularizations. The accurate, efficient and reliable prediction of quantities in turbulent flows is a problem of fundamental importance in many applications ranging from global climate change, homeland security (dispersion of biological or chemical agents), pollution dispersal, energy efficiency and biomedical device design. Large eddy simulation is an approach to turbulent flows in which the large features are separated from the fine details of a flow for a numerical simulation. Hard-won experience and understanding has grown in large eddy simulation so that the methods can now successfully simulate benchmark turbulent flows efficiency and reliably. Scientific and industrial applications are systems of fluid flow equations coupled to other physical effects. These require even greater efficiency and accuracy than benchmark turbulent flow problems. To make progress into these industrial and scientific applications, large eddy simulation now requires systematic methods for assessing sensitivity and uncertainty as well as methods for interrogating the large amounts of data coming out of the finer meshes on faster computers with larger memories. These issues are the focus of the proposed research. Training PhD students to contribute to this important, difficult, interdisciplinary, fascinating and beautiful area is a large part of the proposed effort.