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Title: Non-Equilibrium Dynamics of Discrete Time Boltzmann Systems
Authors: Packwood, David
Supervisors: Gorban, Alexander
Award date: 1-Jun-2012
Presented at: University of Leicester
Abstract: Lattice Boltzmann methods are a fully discrete model and numerical method for simulating fluid dynamics, historically they have been developed as a continuation of lattice gas systems. Another route to a lattice Boltzmann system is a discrete approximation to the Boltzmann equation. An analysis of lattice Boltzmann systems is usually performed from one of these directions. In this thesis the lattice Boltzmann method is presented ab initio as a fully discrete system in its own right. Using the Invariant Manifold hypothesis the microscopic and macroscopic fluid dynamics arising from such a model are found. In particular this analysis represents a validation for lattice Boltzmann methods far from equilibrium. Far from equilibrium, at high Reynolds or Mach numbers, lattice Boltzmann methods can exhibit stability problems. In this work a conditional stability theorem for lattice Boltzmann methods is established. Furthermore several practical numerical techniques for stabilizing lattice Boltzmann schemes are tested.
Type: Thesis
Level: Doctoral
Qualification: PhD
Rights: Copyright © the author, 2012
Appears in Collections:Theses, Dept. of Mathematics
Leicester Theses

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