Since the inception of Computational Fluid Dynamics, turbulence modeling 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. Our group pursues a radically different philosophy in its belief that in order to substantially increase the computational efficiency of turbulent flow simulations and improve the accuracy of predictions of flow characteristics, numerical methods, mesh generation and physics-based modeling need to be tightly integrated to ensure better capturing of the flow physics on a near optimal adaptive anisotropic computational grid, ultimately leading to substantial reduction in the computational cost, while resolving dynamically dominant flow structures.

Latest advancements in wavelet-based adaptive multi-resolution methodologies for the solution of partial differential equations, combined with the unique properties of wavelet analysis to unambiguously identify and isolate localized dynamically dominant flow structures, make it feasible to develop a cardinally different framework for hierarchical modeling and simulation of turbulent flows that fully utilizes spatial/temporal turbulent flow intermittency and tightly integrates numerical methods and physics-based modeling. The integration is achieved by combining spatially and temporally varying wavelet thresholding with hierarchical wavelet-based turbulence modeling. The resulting approach provides automatic smooth transition from directly resolving all flow physics to capturing only the energetic/coherent structures, leading to a dynamically adaptive variable fidelity approach.  Our current efforts are focused on the development of  the unified framework  that will allow for synergistic transition among models of different hierarchy, namely, the adaptive Wavelet-based DNS, the Adaptive wall-resolved LES, Adaptive wall-modeled LES, and adaptive wavelet-based Unsteady RANS and application of the approach to modeling and simulation of industrially relevant flows.