Date of Award

Spring 1-1-2012

Document Type


Degree Name

Doctor of Philosophy (PhD)


Mechanical Engineering

First Advisor

Oleg V. Vasilyev

Second Advisor

Gregory Beylkin

Third Advisor

Henry Tufo

Fourth Advisor

Kurt Karl Maute

Fifth Advisor

Alireza Doostan


The current work develops a wavelet-based adaptive variable fidelity approach that integrates Wavelet-based Direct Numerical Simulation (WDNS), Coherent Vortex Simulations (CVS), and Stochastic Coherent Adaptive Large Eddy Simulations (SCALES). The proposed methodology employs the notion of spatially and temporarily varying wavelet thresholding combined with hierarchical wavelet-based turbulence modeling. The transition between WDNS, CVS, and SCALES regimes is achieved through two-way physics-based feedback between the modeled SGS dissipation (or other dynamically important physical quantity) and the spatial resolution. The feedback is based on spatio-temporal variation of the wavelet threshold, where the thresholding level is adjusted on the fly depending on the deviation of local significant SGS dissipation from the user prescribed level. This strategy overcomes a major limitation for all previously existing wavelet-based multi-resolution schemes: the global thresholding criterion, which does not fully utilize the spatial/temporal intermittency of the turbulent flow. Hence, the aforementioned concept of physics-based spatially variable thresholding in the context of wavelet-based numerical techniques for solving PDEs is established. The procedure consists of tracking the wavelet thresholding-factor within a Lagrangian frame by exploiting a Lagrangian Path-Line Diffusive Averaging approach based on either linear averaging along characteristics or direct solution of the evolution equation. This innovative technique represents a framework of continuously variable fidelity wavelet-based space/time/model-form adaptive multiscale methodology. This methodology has been tested and has provided very promising results on a benchmark with time-varying user prescribed level of SGS dissipation. In addition, a longtime effort to develop a novel parallel adaptive wavelet collocation method for numerical solution of PDEs has been completed during the course of the current work. The scalability and speedup studies of this powerful parallel PDE solver are performed on various architectures. Furthermore, Reynolds scaling of active spatial modes of both CVS and SCALES of linearly forced homogeneous turbulence at high Reynolds numbers is investigated for the first time. This computational complexity study, by demonstrating very promising slope for Reynolds scaling of SCALES even at constant level of fidelity for SGS dissipation, proves the argument that SCALES as a dynamically adaptive turbulence modeling technique, can offer a plethora of flexibilities in hierarchical multiscale space/time adaptive variable fidelity simulations of high Reynolds number turbulent flows.