Wong Chak-fu. / "September 2004." / Thesis (Ph.D.)--Chinese University of Hong Kong, 2004. / Includes bibliographical references (p. 451-475). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web. / Abstracts in English and Chinese.

This paper is about the computation of the stresses on a rigid body from a knowledge of the far field velocities in exterior Stokes and Oseen flows. The surface of the body is assumed to be bounded and smooth, and the body is assumed to move with constant velocity. We give fundamental solutions and derive boundary integral equations for the stresses. As it turns out, these integral equations are singular, and their null space is spanned by the normal to the body. We then discretize the problem by replacing the body by an approximating polyhedron with triangular faces. Using a collocation method, each integral equation delivers a linear system. Since its matrix approximates a singular integral operator, the matrix is ill-conditioned, and the solution is unstable. However, since we know that the problem is uniquely solvable in the hyperspace orthogonal to the normal, we use regularization methods to get stable solutions and project them in the normal direction onto the hyperspace. / Graduation date: 1999

University of Macau / Faculty of Science and Technology / Department of Electromechanical Engineering

No description available.

Accurate and efficient numerical algorithms for solving the three dimensional Navier Stokes equations with a generalized thermodynamic and chemistry model and a one equation turbulence model on structured and unstructured mesh topologies are presented. In the thermo-chemical modeling, particular attention is paid to the modeling of the chemical source terms, modeling of equilibrium thermodynamics, and the modeling of the non-equilibrium vibrational energy source terms. In this work, nonequilibrium thermo-chemical models are applied in the unstructured environment for the first time. A three-dimensional, second-order accurate k-exact reconstruction algorithm for the inviscid and viscous fluxes is presented. Several new methods for determining the stencil required for the inviscid and viscous k-exact reconstruction are discussed. A new simplified method for the computation of the viscous fluxes is also presented. Implementation of the one equation Spalart and Allmaras turbulence model is discussed. In particular, an new integral formulation is developed for this model which allows flux splitting to be applied to the resulting convective flux. Solutions for several test cases are presented to verify the solution algorithms discussed. For the thermo-chemical modeling, inviscid solutions to the three dimensional Aeroassist Flight Experiment vehicle and viscous solutions for the axi-symmetric Ram-II C are presented and compared to experimental data and/or published results. For the hypersonic AFE and Ram-II C solutions, focus is placed on the effects of the chemistry model in flows where ionization and dissociation are dominant characteristics of the flow field. Laminar and turbulent solutions over a flat plate are presented and compared to exact solutions and experimental data. Three dimensional higher order solutions using the k-exact reconstruction technique are presented for an analytic forebody. / Ph. D.

A weakly nonlinear stability analysis was conducted for the flow induced in an incompressible, Newtonian, viscous fluid lying between two infinite parallel plates which form a channel. The plates are oscillating synchronously in simple harmonic motion. The disturbed velocity of the flow was written in the form of a series in powers of a parameter which is a measure of the distance away from the linear theory neutral conditions. The individual terms of this series were decomposed using Floquet theory and Fourier series in time. The equations at second order and third order in were derived, and solutions for the Fourier coefficients were found using pseudospectral methods for the spatial variables. Various alternative methods of computation were applied to check the validity of the results obtained. The Landau equation for the amplitude of the disturbance was obtained, and the existence of equilibrium amplitude solutions inferred. The values of the coefficients in the Landau equation were calculated for the nondimensional channel half-widths h for the cases h = 5, 8, 10, 12, 14 and 16. It was found that equilibrium amplitude solutions exist for points in wavenumber Reynolds number space above the smooth portion of the previously determined linear stability neutral curve in all the cases examined. Similarly, Landau coefficients were calculated on a special feature of the neutral curve (called a ???finger???) for the case h = 12. Equilibrium amplitude solutions were found to exist at points inside the finger, and in a particular region outside near the top of the finger. Traces of the x-components of the disturbance velocities have been presented for a range of positions across the channel, together with the size of the equilibrium amplitude at these positions. As well, traces of the x-component of the velocity of the disturbed flow and traces of the velocity of the basic flow have been given for comparison at a particular position in the channel.

This thesis is on the existence and uniqueness of weak solutions to the Navier-Stokes equations in R3 which govern the velocity of incompressible fluid with viscosity ν. The solution is obtained in the space of tempered distributions on R3 given an initial condition and forcing data which are dominated by majorizing kernels. The solution takes the form of an expectation of functionals on a Markov process indexed by a binary branching tree. / Graduation date: 2012

In this thesis, we consider soltions to the two-dimensional Euler equations with uniformly continuous initial vorticity in a critical or subcritical Besov space. We use paradifferential calculus to show that the solution will lose an arbitrarily small amount of smoothness over any fixed finite time interval. This result is motivated by a theorem of Bahouri and Chemin which states that the Sobolev exponent of a solution to the two-dimensional Euler equations in a critical or subcritical Sobolev space may decay exponentially with time. To prove our result, one can use methods similar to those used by Bahouri and Chemin for initial vorticity in a Besov space with Besov exponent between 0 and 1; however, we use different methods to prove a result which applies for any Sobolev exponent between 0 and 2. The remainder of this thesis is based on joint work with J. Kelliher. We study the vanishing viscosity limit of solutions of the Navier-Stokes equations to solutions of the Euler equations in the plane assuming initial vorticity is in a variant Besov space introduced by Vishik. Our methods allow us to extend a global in time uniqueness result established by Vishik for the two-dimensional Euler equations in this space. / text

No description available.

A weakly nonlinear stability analysis was conducted for the flow induced in an incompressible, Newtonian, viscous fluid lying between two infinite parallel plates which form a channel. The plates are oscillating synchronously in simple harmonic motion. The disturbed velocity of the flow was written in the form of a series in powers of a parameter which is a measure of the distance away from the linear theory neutral conditions. The individual terms of this series were decomposed using Floquet theory and Fourier series in time. The equations at second order and third order in were derived, and solutions for the Fourier coefficients were found using pseudospectral methods for the spatial variables. Various alternative methods of computation were applied to check the validity of the results obtained. The Landau equation for the amplitude of the disturbance was obtained, and the existence of equilibrium amplitude solutions inferred. The values of the coefficients in the Landau equation were calculated for the nondimensional channel half-widths h for the cases h = 5, 8, 10, 12, 14 and 16. It was found that equilibrium amplitude solutions exist for points in wavenumber Reynolds number space above the smooth portion of the previously determined linear stability neutral curve in all the cases examined. Similarly, Landau coefficients were calculated on a special feature of the neutral curve (called a ???finger???) for the case h = 12. Equilibrium amplitude solutions were found to exist at points inside the finger, and in a particular region outside near the top of the finger. Traces of the x-components of the disturbance velocities have been presented for a range of positions across the channel, together with the size of the equilibrium amplitude at these positions. As well, traces of the x-component of the velocity of the disturbed flow and traces of the velocity of the basic flow have been given for comparison at a particular position in the channel.