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Date of Award


Document Type

Campus Access Dissertation

Degree Name

Doctor of Philosophy in Mathematical Sciences (PhD)

Administrative Home Department

Department of Mathematical Sciences

Advisor 1

Alexander E. Labovsky

Committee Member 1

Yang Yang

Committee Member 2

Cécile Piret

Committee Member 3

Aleksey Smirnov


In Labovsky (2020), a new family of turbulence models named Large Eddy Simulation with Correction (LES-C) has been proposed to reduce the modeling error of Large Eddy Simulation (LES) models. There a predictor-corrector technique called defect correction was used, treating a Large Eddy Simulation(LES) model as the defect solution and then correcting it on the same spatial mesh in the correction step. Chapter 2, Chapter 4, and Chapter 5 of this dissertation are based on the studies on LES-C models. Chapter 2 presents a model to reduce the time discretization error of the LES-C models using the deferred correction technique. Since the temporal accuracy was gained by adding several terms to the right-hand side of the correction step of the existing LES-C structure, the accuracy was gained at no additional computational cost. It was demonstrated using the Approximate Deconvolution Model (ADM) in the LES family and the new model was named ADC with deferred correction. Chapter 3 describes the effect of the standard and modular grad-div stabilization with Taylor-Hood finite elements on drag/lift coefficient comparing it with the calculations of Scott-Vogelius finite elements. The Chapter 4 proposes a model to improve the accuracy of the MagnetoHydroDynamic(MHD) system that is written in Els´asser variables. It was developed in the LES-C framework aiming to reduce both temporal and modeling errors of the existing turbulent model. It was demonstrated using ADM(MHD-ADM) in the LES family and through the numerical tests it was shown the superiority of the new model MHD- ADC over MHD-ADM. The Chapter 5 investigates four LES-C models namely ADC, Leray-α-C, NS-α-C, and NS-ω-C which developed from the popular LES models ADM, Leray-α, NS-α, and NS-ω by performing the analysis for three benchmark problems: flow past a circular object, flow past a step, and benchmark problem of turbulent 3D channel flow.