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The lattice Boltzmann method for complex flows

Reis, Tim 2007. The lattice Boltzmann method for complex flows. PhD Thesis, Cardiff University.
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Abstract

This thesis presents the extension of the lattice Boltzmann equation (LBE) to several well-known flows. First, the flow over a cylinder is studied using the LBE and the numerical predictions are shown to compare well with those obtained using a stylised finite volume method. A clear and formal perturbation analysis of the generalised LBE is also presented. A LBE for axisymmetric flows is developed, the precise form of which is derived through a Chapman-Enskog analysis so that the additional axisymmetric contributions to the Navier-Stokes equation are furnished when written in the cylindrical polar coordinate system. Stokes' flow over a sphere is studied and excellent agreement is found between the numerical and analytical predictions. A lattice Boltzmann model for immiscible binary fluids with variable viscosities and density ratio is developed. In the macroscopic limit this model is shown to recover the Navier-Stokes equations for two phase flow. A theoretical expression for surface tension is determined. The validity of this analysis is confirmed by comparing numerical and theoretical predictions of surface tension as a function of density. A number of numerical simulations are presented and shown to be in good agreement with analytical results. Finally, an axisymmetric multiphase lattice Boltzmann model has been proposed. This model is easy to implement and some test cases have been performed to demonstrate its capabilities. A review of the extension of the lattice Boltzmann equation to viscoelasticity is also presented.

Item Type: Thesis (PhD)
Status: Unpublished
Schools: Mathematics
Subjects: Q Science > QA Mathematics
Date of First Compliant Deposit: 30 March 2016
Last Modified: 30 Apr 2013 09:47
URI: http://orca.cf.ac.uk/id/eprint/46827

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