Latest advancements in wavelet-based numerical 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 propose development of intelligent methods for turbulent flow simulation that tightly integrate numerics and physicsbased modeling. The overall goal of the research is to develop a robust and computationally efficient predictive computational approach, capable of performing variable fidelity numerical simulation of transitional and turbulent incompressible flows for different flow conditions including turbulent flow separation, turbulent boundary layers, shear layers, and jets. Spatially variable wavelet thresholding strategy will be used for model form adaptation. The wavelet threshold will evolve in space and time using feedback control to guarantee that only a priori specified fraction of turbulent kinetic energy or turbulence dissipation rate is resolved. With such a strategy the transition between adaptive Wavelet-based Direct Numerical Simulation (WDNS), the Coherent Vortex Simulation (CVS), the Stochastic Coherent Adaptive Large Eddy Simulation (SCALES), and adaptive Wavelet-based Unsteady Reynolds Averaged Navier-Stokes (WURANS) simulations regimes is natural: the WURANS models switch to subgrid scale model for SCALES to no model for CVS and WDNS approaches as the percentage of the resolved turbulent kinetic energy or resolved turbulence dissipation rate increases from 0% to 100%. This will form a basis for the proposed new physics-based integration of WDNS, CVS, SCALES, and WURANS methodologies. The strength of the proposed methodology is that all models (WDNS, CVS, SCALES, WURANS) use the same wavelet based adaptation strategy to resolve and tracks the energy-containing eddies on the adaptive computational mesh. The approach will be further enhanced by integrating it with Brinkman penalization to enforce solid boundaries of arbitrary complexity. A unique advantage of combining the proposed approach with Brinkman penalization is the ability to enforce boundary conditions to a specified precision without a significant computational overhead. The proposed hierarchical variable fidelity approach will be extensively validated for a number of benchmark problems such as turbulent channel flow, turbulent flow over backward facing step, turbulent flow in a planar asymmetric diffuser, and turbulent flow past circular and square cylinders. The algorithms developed herein specifically address problems of efficient and affordable numerical simulations of turbulent flows, when classical methods have failed to yield progress in reliable predictive modeling. The research will push the envelope of computational capabilities of modeling multi-scale physics of high Reynolds number turbulent flows and will make possible the simulations of high Reynolds number turbulent flows, which currently are difficult or impossible to solve using conventional numerical algorithms. It is expected that the research will provide insight into the complex multi-scale physics of turbulent flows, improve our understanding of fluid turbulence, and even provide engineers with a vital design tool that completely eliminates the onerous overhead of current grid generation methods. An additional aim of this project is in education and dissemination of the newly developed approach and in distribution of the software tools to be developed as a part of the project for the wide use by the scientific community including government laboratories. The new integrated eddy capturing approach has potentially revolutionary impact on all technological endeavors in which turbulent flow plays an important role. Aeronautics, propulsion, transportation and energy are just a few potential areas for this. The range of other applications in free-surface flows, MHD, and nonlinear PDEs in general is tremendous. High resolution results generated as a part of this project are expected to be broadly used by the scientific community.
