Date of Award

Spring 1-1-2016

Document Type


Degree Name

Doctor of Philosophy (PhD)


Mechanical Engineering

First Advisor

Oleg V. Vasilyev

Second Advisor

Peter Hamlington

Third Advisor

Daven Henze

Fourth Advisor

Alireza Doostan

Fifth Advisor

John A. Evans


Turbulent flows, noted for their chaotic dynamic and multiscale nature, are notoriously difficult and expensive to simulate accurately for problems of engineering interest. Adaptive wavelet-based methods have shown promise to this end with their ability to efficiently resolve local, coherent structures with a priori accuracy control. Here the methods are extended to the compressible regime, where thermodynamic and variable density effects interact with the turbulent flow.

The adaptive wavelet collocation method (AWCM) exploits spatio-temporal intermittency in turbulent flows through multiresolution analysis. The highest fidelity approaches, wavelet-based direct numeric simulation and coherent vortex simulation, capture all scales of the energy cascade. The so called stochastic-coherent adaptive large eddy simulation (SCALES) method, however, requires the implementation of a subgrid-scale (SGS) model. A compressible kinetic energy equation-based approach and a minimum dissipation model are adapted to the SCALES framework. For the k-equation model, nonlinear filtered terms are scaled by the SGS kinetic energy and model coefficients are locally determined through dynamic procedures. Stability of turbulent stress and heat flux is enhanced by the SGS kinetic energy field, allowing backscatter of modeled terms.

This work seeks to extend the capabilities of AWCM towards flow of engineering interest. In order to efficiently simulate bounded, complex geometry flows using a proposed hybrid adaptive-wavelet/curvilinear coordinate approach. The AWCM has a notable shortcoming in that mesh refinement is isotropic. A coordinate system transform can be used to stretch the grid and introduce local anisotropy, more effectively resolving arbitrarily oriented boundary layers while still preserving the rectilinear computational space necessary for the adaptive wavelet transform. A volume penalization method for compressible flows has been developed to introduce solid surfaces with arbitrary boundary conditions.