Cook, Charles2024-04-242024-04-242024-04-23vt_gsexam:39164https://hdl.handle.net/10919/118656The 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.ETDenCreative Commons Attribution-NonCommercial-ShareAlike 4.0 InternationalComputational Fluid DynamicsFinite Element MethodsCompressible FlowLattice Boltzmann MethodsDissertation