Award Date

May 2023

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Mathematical Sciences

First Committee Member

Monika Neda

Second Committee Member

Pengtao Sun

Third Committee Member

Jichun Li

Fourth Committee Member

Hongtao Yang

Fifth Committee Member

Angel Muleshkov

Sixth Committee Member

Haroon Stephen

Number of Pages

120

Abstract

It is often the case when attempting to capture real word phenomena that the resulting mathematical model is too difficult and even not feasible to be solved analytically. As a result, a computational approach is required and there exists many different methods to numerically solve models described by systems of partial differential equations. The Finite Element Method is one of them and it was pursued herein.This dissertation focuses on the finite element analysis and corresponding numerical computations of several different models. The first part consists of a study on two different fluid flow models: the main governing model of fluid dynamics, i.e. the Navier Stokes equations (NSE), and a large eddy simulation model, i.e. the Generalized Smagorinsky model (GSM). For the NSE we investigated the effects of using the EMAC formulation on projection method discretization. The study of the enhanced GSM model includes a comparison with the classical Smagorinsky Model to monitor for tangible improvement. Finite element analyses, such as stability and error estimates, are derived for both discretization of the models, NSE and GSM. That is followed by computations for benchmark problems. The second part examines a traffic model, the so-called Lighthill-Whitham-Richards (LWR) model, in the case of linear advection and the nonlinear Greenshields model advection. This LWR model is studied in a biological context phenomena of bio-polymerization for protein synthesis. Numerical analysis and simulations are investigated and presented.

Keywords

Finite element method; Lighthill-Whitham-Richards Model; Mathematical modeling; Navier-Stokes equations; Numerical analysis

Disciplines

Aerodynamics and Fluid Mechanics | Applied Mathematics | Mathematics

Degree Grantor

University of Nevada, Las Vegas

Language

English

Rights

IN COPYRIGHT. For more information about this rights statement, please visit http://rightsstatements.org/vocab/InC/1.0/

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