The Quantized Velocity Finite Element Method

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dc.contributor.authorCook, Charlesen
dc.contributor.committeechairKapania, Rakesh K.en
dc.contributor.committeememberMassa, Lucaen
dc.contributor.committeememberStremler, Mark A.en
dc.contributor.committeememberKauffman, Justinen
dc.contributor.departmentEngineering Science and Mechanicsen
dc.date.accessioned2024-04-24T16:47:52Zen
dc.date.available2024-04-24T16:47:52Zen
dc.date.issued2024-04-23en
dc.description.abstractThe 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.en
dc.description.abstractgeneralTo 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.en
dc.description.degreeDoctor of Philosophyen
dc.format.mediumETDen
dc.identifier.othervt_gsexam:39164en
dc.identifier.urihttps://hdl.handle.net/10919/118656en
dc.language.isoenen
dc.publisherVirginia Techen
dc.rightsCreative Commons Attribution-NonCommercial-ShareAlike 4.0 Internationalen
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/4.0/en
dc.subjectComputational Fluid Dynamicsen
dc.subjectFinite Element Methodsen
dc.subjectCompressible Flowen
dc.subjectLattice Boltzmann Methodsen
dc.titleThe Quantized Velocity Finite Element Methoden
dc.typeDissertationen
thesis.degree.disciplineEngineering Mechanicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.leveldoctoralen
thesis.degree.nameDoctor of Philosophyen

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