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Title: Techniques for modelling incompressible fluid flow
Author: Roberts, William
Awarding Body: University of Edinburgh
Current Institution: University of Edinburgh
Date of Award: 1991
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The work presented in this thesis can be divided into two main parts: a study of Cellular Automaton (CA) models of incompressible fluid flow and work on the use of Renormalisation Group (RG) methods to derive an effective viscosity for use in subgrid modelling in Large Eddy Simulation of incompressible turbulence. The derivation of hydrodynamic equations for the behaviour of CA models is reviewed in the context of classical statistical mechanics. In computer simulations of such models, velocity and density values are found by calculating averages of appropriate microscopic quantities: the effect of this averaging on noise levels in such simulations is investigated. We verify the expected results that the noise level is proportional to N-1/2 where N is the number of space cells or time-steps in the average. A new CA model, the '2D multispeed model', is developed by considering the projection of the 4D face-centred hypercubic model into 2D. Optimal collision rules are obtained and computer simulations of flow through a channel are performed, which reproduce the well-known parabolic velocity profile. Kinematic viscosity is calculated as a function of particle density from the velocity profiles and the imposed pressure gradient: the results compare favourably with those of the FHP model in terms of maximum attainable Reynolds number for a given computational effort. After briefly summarising some important aspects of turbulent fluid flow, a conditional averaging procedure is presented, designed to deal with the problems of coupling between low-wavenumber and high-wavenumber modes in the filtered Navier-Stokes equation in k-space. The conditional average is precisely defined in terms of the turbulent ensemble and a method of evaluation is proposed, whereby the conditional average of moments of the velocity field is related to the full-ensemble average of the same quantities, with an explicit error term representing the effect of the coupling. The application of this averaging procedure to the modelling of small-scale motion in homogeneous isotropic turbulence is explained and the derivation of an effective viscosity, due to McComb and Watt (Phys. Rev. Lett. 65 (1990) p.3281) is outlined.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available