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Full-Text Articles in Physical Sciences and Mathematics
Topics In Mode Conversion Theory And The Group Theoretical Foundations Of Path Integrals, Andrew Stephen Richardson
Topics In Mode Conversion Theory And The Group Theoretical Foundations Of Path Integrals, Andrew Stephen Richardson
Dissertations, Theses, and Masters Projects
This dissertation reports research about the phase space perspective for solving wave problems, with particular emphasis on the phenomenon of mode conversion in multicomponent wave systems, and the mathematics which underlie the phase space perspective. Part I of this dissertation gives a review of the phase space theory of resonant mode conversion. We describe how the WKB approximation is related to geometrical structures in phase space, and how in particular ray-tracing algorithms can be used to construct the WKB solution. We further review how to analyze the phenomena of mode conversion from the phase space perspective. By making an expansion …
Methods For Stabilizing High Reynolds Number Lattice Boltzmann Simulations, Brian Robert Keating
Methods For Stabilizing High Reynolds Number Lattice Boltzmann Simulations, Brian Robert Keating
Dissertations, Theses, and Masters Projects
The Lattice Boltzmann Method (LBM) is a simple and highly efficient method for computing nearly incompressible fluid flow. However, it is well known to suffer from numerical instabilities for low values of the transport coefficients. This dissertation examines a number of methods for increasing the stability of the LBM over a wide range of parameters. First, we consider a simple transformation that renders the standard LB equation implicit. It is found that the stability is largely unchanged. Next, we consider a stabilization method based on introducing a Lyapunov function which is essentially a discrete-time H-function. The uniqueness of an H-function …