General-domain compressible Navier-Stokes solvers exhibiting quasi-unconditional stability and high-order accuracy in space and time

This thesis presents a new class of solvers for the subsonic compressible Navier-Stokes equations in general two- and three-dimensional spatial domains. The proposed methodology incorporates: 1) A novel linear-cost implicit solver based on use of higher-order backward differentiation formulae (BDF) and the alternating direction implicit approach (ADI); 2) A fast explicit solver; 3) Dispersionless spectral spatial discretizations; and 4) A domain decomposition strategy that negotiates the interactions between the implicit and explicit domains. In particular, the implicit methodology is quasi-unconditionally stable (it does not suffer from CFL constraints for adequately resolved flows), and it can deliver orders of time accuracy between two and six in the presence of general boundary conditions. In fact this thesis presents, for the first time in the literature, high-order time-convergence curves for Navier-Stokes solvers based on the ADI strategy---previous ADI solvers for the Navier-Stokes equations have not demonstrated orders of temporal accuracy higher than one. An extended discussion is presented in this thesis which places on a solid theoretical basis the observed quasi-unconditional stability of the methods of orders two through six. The performance of the proposed solvers is favorable. For example, a two-dimensional rough-surface configuration including boundary layer effects at Reynolds number equal to one million and Mach number 0.85 (with a well-resolved boundary layer, run up to a sufficiently long time that single vortices travel the entire spatial extent of the domain, and with spatial mesh sizes near the wall of the order of one hundred-thousandth the length of the domain) was successfully tackled in a relatively short (approximately thirty-hour) single-core run; for such discretizations an explicit solver would require truly prohibitive computing times. As demonstrated via a variety of numerical experiments in two- and three-dimensions, further, the proposed multi-domain parallel implicit-explicit implementations exhibit high-order convergence in space and time, useful stability properties, limited dispersion, and high parallel efficiency.

O divisor de águas da política imperial: D. Pedro II, a conciliação e o Marquês de Paraná (1853-1856)

A Conciliação política foi um tema muito altercado no meado do Oitocentos no Segundo Reinado brasileiro. Este debate fora intensamente travado entre os principais partidos imperiais, Liberal e Conservador, que se alternavam no poder ao longo de quase 50 anos de comando do imperador D. Pedro II. Sobre seu governo, considerado por Joaquim Nabuco como a Grande Era Brasileira, é que este autor legou à historiografia posterior a sua obra máxima: Um Estadista do Império. Nossa dissertação parte da seguinte premissa: D. Pedro II no desejo de reinar, governar e administrar, acima dos partidos, encetou o seu Pensamento Augusto, isto é, a Conciliação. Os liberais acusavam a Conciliação de esvaziar suas propostas ao serem implementadas pelos conservadores. Estes que se encontravam no poder desde 1848, liderados pelos saquaremas, rechaçaram completamente tal ideia, pois entendiam que esta política patrocinada pela Coroa poderia enfraquecer seu partido. O Receio virou realidade, mediante algumas das medidas tomadas pelo Gabinete, pois para tal empreendimento, de compor um ministério com políticos liberais e conservadores, a Coroa contou com Honório Hermeto Carneiro Leão, Marquês de Paraná, para chefiar o primeiro gabinete conciliatório da história do Segundo Reinado enfrentando várias resistências, principalmente entre os referidos saquaremas. O sucesso do gabinete creditou-se à força, tato e prudência do Marquês e, principalmente, ao pensamento do Imperador. A partir daí a história política do Segundo Reinado tomou novas feições.

I. Stokes flow past a thin screen. II. Viscous flows past porous bodies of finite size

Part I

The slow, viscous flow past a thin screen is analyzed based on Stokes equations. The problem is reduced to an associated electric potential problem as introduced by Roscoe. Alternatively, the problem is formulated in terms of a Stokeslet distribution, which turns out to be equivalent to the first approach.

Special interest is directed towards the solution of the Stokes flow past a circular annulus. A "Stokeslet" formulation is used in this analysis. The problem is finally reduced to solving a Fredholm integral equation of the second kind. Numerical data for the drag coefficient and the mean velocity through the hole of the annulus are obtained.

Stokes flow past a circular screen with numerous holes is also attempted by assuming a set of approximate boundary conditions. An "electric potential" formulation is used, and the problem is also reduced to solving a Fredholm integral equation of the second kind. Drag coefficient and mean velocity through the screen are computed.

Part II

The purpose of this investigation is to formulate correctly a set of boundary conditions to be prescribed at the interface between a viscous flow region and a porous medium so that the problem of a viscous flow past a porous body can be solved.

General macroscopic equations of motion for flow through porous media are first derived by averaging Stokes equations over a volume element of the medium. These equations, including viscous stresses for the description, are more general than Darcy's law. They reduce to Darcy's law when the Darcy number becomes extremely small.

The interface boundary conditions of the first kind are then formulated with respect to the general macroscopic equations applied within the porous region. An application of such equations and boundary conditions to a Poiseuille shear flow problem demonstrates that there usually exists a thin interface layer immediately inside the porous medium in which the tangential velocity varies exponentially and Darcy's law does not apply.

With Darcy's law assumed within the porous region, interface boundary conditions of the second kind are established which relate the flow variables across the interface layer. The primary feature is a jump condition on the tangential velocity, which is found to be directly proportional to the normal gradient of the tangential velocity immediately outside the porous medium. This is in agreement with the experimental results of Beavers, et al.

The derived boundary conditions are applied in the solutions of two other problems: (1) Viscous flow between a rotating solid cylinder and a stationary porous cylinder, and (2) Stokes flow past a porous sphere.

An indexed bibliography of papers on tagging of tunas and billfishes

Two working parties, the Working Party on Tuna Tagging in the Pacific and Indian Oceans and the Working Party on Tuna Tagging in the Atlantic and Adjacent Seas, were formed by the Food and Agriculture Organization (FAD) of the United Nations in 1966 (Anonymous, 1966c). The conveners of these working parties were Dr. James Joseph of the Inter-American Tropical Tuna Commission (IATTC) and Mr. FrankJ. Mather, III, of the Woods Hole Oceanographic Institution (WHOI). In 1969 it was recommended that the working parties direct their attention toward billfishes, as well as tunas (Anonymous, 1969h: 5). One report (Joseph and working party, 1969) was published by the Pacific and Indian Oceans group and two (Mather and working party, 1969 and 1972) were published by the Atlantic Ocean and adjacent seas group. Each of the three working party reports included a bibliography of tuna and billfish tagging. The compiler of this bibliography, beginning in 1970, prepared numerous memoranda to the members of the working party, most of which included lists of papers on tuna and billfish tagging which had come to his attention, either directly or through members of the working party. The bibliographies in the three working party reports and the lists of references in the memoranda form the basis for the present bibliography.