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. / Doctor of Philosophy / To model any of the four fundamental states of matter, for practical engineering applications, we must first recognize the complexity of such states. In consequence, a new and novel approach is presented on how to numerically simulate the dynamics of a gas using both the Euler and Navier-Stokes-Fourier equations of continuum mechanics and thermodynamics. In contrast to direct numerical simulation, a statistical mechanical prescription will be given where the equations of motion will be quantized using methods taken from the study of quantum mechanics. This newly developed discretization of the phase space and time, or phasetime, provides optimal stability for compressible flow simulations. From the newly proposed framework, the 7D phasetime element has been born.
| Identifer | oai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/118656 |
| Date | 23 April 2024 |
| Creators | Cook, Charles |
| Contributors | Engineering Science and Mechanics, Kapania, Rakesh K., Massa, Luca, Stremler, Mark A., Kauffman, Justin |
| Publisher | Virginia Tech |
| Source Sets | Virginia Tech Theses and Dissertation |
| Language | English |
| Detected Language | English |
| Type | Dissertation |
| Format | ETD, application/pdf |
| Rights | Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International, http://creativecommons.org/licenses/by-nc-sa/4.0/ |
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