The Quantized Velocity Finite Element Method

The Euler and Navier-Stokes-Fourier equations will be directly expressed as distribution evolution equations, where a new and proper continuum prescription will be derived. These equations of motion will be numerically solved with the development of a new and unique finite element formulation. Out of this framework, the 7D phasetime element has been born. To provide optimal stability, a new quantization procedure is established based on the principles of quantum theory. The entirety of this framework has been coined the "quantized velocity finite element method" (QVFEM). The work performed herein lays the foundational development of what is hoped to become a new paradigm shift in computational fluid dynamics.

Name thesis:degree_name

Doctor of Philosophy

Level thesis:degree_level

doctoral

Discipline thesis:degree_discipline

Engineering Mechanics

Department dc:contributor.department

Engineering Science and Mechanics

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

2024

Author dc:creator

• Cook, Charles

Chair dc:contributor.committeechair

• Kapania, Rakesh K.

Committee members dc:contributor.committeemember

• Massa, Luca
• Stremler, Mark A.
• Kauffman, Justin

• Computational Fluid Dynamics
• Finite Element Methods
• Compressible Flow
• Lattice Boltzmann Methods

Statement dc:rights

• Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International

Licence dc:rights.uri

• http://creativecommons.org/licenses/by-nc-sa/4.0/

Language dc:language.iso

en

Dc Identifier Other

vt_gsexam:39164

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/118656