Perfectly Matched Layer Absorbing Boundary Conditions for the Discrete Velocity Boltzmann-BGK Equation

<p>Perfectly Matched Layer (PML) absorbing boundary conditions were first proposed by Berenger in 1994 for the Maxwell's equations of electromagnetics. Since Hu first applied the method to Euler's equations in 1996, progress made in the application of PML to Computational Aeroacoustics (CAA) includes linearized Euler equations with non-uniform mean flow, non-linear Euler equations, flows with an arbitrary mean flow direction, and non-linear clavier-Stokes equations. Although Boltzmann-BGK methods have appeared in the literature and have been shown capable of simulating aeroacoustics phenomena, very little has been done to develop absorbing boundary conditions for these methods. The purpose of this work was to extend the PML methodology to the discrete velocity Boltzmann-BGK equation (DVBE) for the case of a horizontal mean flow in two and three dimensions. The proposed extension of the PML has been accomplished in this dissertation. Both split and unsplit PML absorbing boundary conditions are presented in two and three dimensions. A finite difference and a lattice model are considered for the solution of the PML equations. The linear stability of the PML equations is investigated for both models. The small relaxation time needed for the discrete velocity Boltzmann-BC4K model to solve the Euler equations renders the explicit Runge-Kutta schemes impractical. Alternatively, implicit-explicit Runge-Kutta (IMEX) schemes are used in the finite difference model and are implemented explicitly by exploiting the special structure of the Boltzmann-BGK equation. This yields a numerically stable solution by the finite difference schemes. As the lattice model proves to be unstable, a coupled model consisting of a lattice Boltzmann (LB) method for the Ulterior domain and an IMEX finite difference method for the PML domains is proposed and investigated. Numerical examples of acoustic and vorticity waves are included to support the validity of the PML equations. In each example, accurate solutions are obtained, supporting the conclusion that PML is an effective absorbing boundary condition.</p>

Name thesis:degree_name

Doctor of Philosophy (PhD)

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics & Statistics

Year dc:date.available

2011

Author dc:creator

• Craig, Elena

Contributors dc:contributor

• Fang Q. Hu
• Chester Grosch
• Richard D. Noren
• Yan Peng
• Hideaki Kaneko

• Absorbing boundary conditions
• Boltzmann-BGK equation
• Discrete velocity
• Perfectly matched layer
• Acoustics, Dynamics, and Controls
• Applied Mathematics
• Physics

Statement dc:rights

• <p>In Copyright. URI: <a href="http://rightsstatements.org/vocab/InC/1.0/">http://rightsstatements.org/vocab/InC/1.0/</a> This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).</p>

Identifier

9781124973098

OAI identifier oai:identifier

oai:digitalcommons.odu.edu:mathstat_etds-1012