Continuously Variable Fidelity Adaptive Large Eddy Simulation

Since the inception of Computational Fluid Dynamics, turbulence model-ing and numerical methods evolved as two separate fields of research with the perception that once a turbulence model is developed, any suitable computational approach can be used for the numerical simulations of the model. Over the last decade, our group has pursued research with cardinally different philosophy in its belief that in order to increase the computational efficiency of turbulent flow simulations and substantially improve the accuracy of predictions of flow characteristics, both the numerics and physics-based modeling need to be tightly integrated to ensure better capturing of the flow physics on a near optimal adaptive computational grid, ultimately leading to substantial reduction in the computational cost, while resolving dynamically dominant flow structures. Turbulence is difficult to approximate mathematically, and to calculate numerically, because it is active over a large and continuous range of length scales (e.g. from less than a millimeter to hundreds of kilometers in the atmosphere). The range of active scales increases with Reynolds number (like í µí±…í µí±’ !/! for three-dimensional turbulence), which means flows are increasingly difficult to calculate at the large Reynolds numbers of practical interest. Although the active flow regions extend over many scales, they are distributed inhomogene-ously in both space and time. This inhomogeneity is called intermittency. This talk will provide an overview of a novel framework for continuously variable fidelity adaptive large eddy simulation that tightly integrates numerics and physics-based modeling and fully exploits the spatial and temporal intermitten-cy of turbulent flows by constructing reduced models of turbulence (e.g. in terms of coherent vortices) and by optimally using a finite number of computational elements (e.g. using adaptive mesh refinement). Latest advancements in wavelet-based numerical methodologies for the solution of partial differential equations [1-4], combined with the unique properties of wavelet analysis to unambiguously identify and isolate localized dynamically dominant flow structures [5-6], and to track them on adaptive computational meshes [7-9], make it feasible to develop intelligent methods for turbulent flow simulation that tightly integrate numerics and physics-based modeling.