Free surface flow simulations using high order algorithms
File(s)
Author(s)
Robertson, Iain
Type
Thesis
Abstract
The aim of this work is to formulate a computational algorithm to simulate the motion of a viscous fluid with a free surface boundary undergoing oscillations of sufficient amplitude to induce nonlinearities. To achieve this aim stability complications caused by the spatial discretisation of a two dimensional fluid domain are investigated by analysing the eigenspectrum of the semi-discrete, linear, inviscid solution system. The conditions for stability are established and procedures to overcome instability are formulated and tested. Unsteady, inviscid flows with nonlinear boundary conditions are then examined. Free surface flows of a viscous, incompressible fluid undergoing unsteady motion are computationally generated using a high order temporal and spatial discretisation scheme to solve the arbitrary Lagrangian-Eulerian Navier-Stokes and continuity equations. The discretisation concepts are presented and the governing equations for fluid flow within a moving frame of reference are formulated.
The suitability of differing free surface boundary conditions is investigated by simulating forced and free oscillations of a contained body of fluid for increasing Reynolds number. The flow structures they promote are compared and the effect of Reynolds number is investigated, in terms of the general flow characteristics and the choice of boundary condition. The dissipative nature of the boundary conditions are compared with analytically predicted decay rates for the oscillation of a free surface under the force of gravity [37]. Various models to overcome the moving free surface contact point and no-slip boundary conditions are devised and their respective merits studied by observing the production of contact wall boundary layers and advected vorticity layers. The additional dissipation generated by the introduction of the formulated contact wall boundary conditions is assessed and compared with analytically predicted decay rates of a freely oscillating bounded fluid [35]. Preliminary three dimensional results are given for free surface flow within a container undergoing forced oscillations. Three dimensional effects are investigated for uni-directional and bi-directional horizontal motion of the containing tank for Re = 111.
The suitability of differing free surface boundary conditions is investigated by simulating forced and free oscillations of a contained body of fluid for increasing Reynolds number. The flow structures they promote are compared and the effect of Reynolds number is investigated, in terms of the general flow characteristics and the choice of boundary condition. The dissipative nature of the boundary conditions are compared with analytically predicted decay rates for the oscillation of a free surface under the force of gravity [37]. Various models to overcome the moving free surface contact point and no-slip boundary conditions are devised and their respective merits studied by observing the production of contact wall boundary layers and advected vorticity layers. The additional dissipation generated by the introduction of the formulated contact wall boundary conditions is assessed and compared with analytically predicted decay rates of a freely oscillating bounded fluid [35]. Preliminary three dimensional results are given for free surface flow within a container undergoing forced oscillations. Three dimensional effects are investigated for uni-directional and bi-directional horizontal motion of the containing tank for Re = 111.
Version
Open Access
Date Issued
2001
Date Awarded
2001
Copyright Statement
Attribution NoDerivatives 4.0 International Licence (CC BY-ND)
Advisor
Sherwin, Spencer
Graham, Mike
Warburton, Tim
Publisher Department
Aeronautics
Publisher Institution
University of London - Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)