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Title: Non-equilibrium dynamics of discrete time Boltzmann
Author: Packwood, David
ISNI:       0000 0004 2723 0850
Awarding Body: University of Leicester
Current Institution: University of Leicester
Date of Award: 2012
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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.
Supervisor: Gorban, Alexander. Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available