Thèse (D.Eng.)--Université du Québec à Chicoutimi, 2001. / Document électronique également accessible en format PDF. CaQCU

Thesis (M.S.)--Mississippi State University. Department of Aerospace Engineering. / Title from title screen. Includes bibliographical references.

Thesis (M.Sc.)--Memorial University of Newfoundland, 2002. / Restricted until May 2003. Bibliography: leaves 98-101.

Thesis (Ph. D.)--Ohio State University, 2005. / Title from first page of PDF file. Document formatted into pages; contains xviii, 178 p.; also includes graphics (some col.) Includes bibliographical references (p. 173-178). Available online via OhioLINK's ETD Center

Thesis (Ph. D.)--University of Texas at Austin, 2005. / Supervisors: Clinton N. Dawson and Yannis Kallinderis. Vita. Includes bibliographical references.

Thesis (Ph. D.)--University of Texas at Austin, 2007. / Vita. Includes bibliographical references.

We introduce new methods based on the L2 Optimal Transport (OT) problem and the Navier-Stokes equations to approximate a fluid velocity field from images obtained with Particle Image Velocimetry (PIV) measurements. The main idea is to consider two successive images as the initial and final densities in the OT problem, and to use the associated OT flow as an estimate of the underlying physical flow. We build a simple but realistic model for PIV data, and use it to analyze the behavior of the transport map in this situation. We then design and implement a series of post-processing filters created to improve the quality of the numerical results, and we establish comparisons with traditional cross-correlation algorithms. These results indicate that the OT-PIV procedure performs well on low to medium seeding densities, and that it gives better results than typical cross-correlation algorithms in some cases. Finally, we use a variational method to project the OT velocity field on the space of solutions of the Navier-Stokes equations, and extend it to the rest of the fluid domain, outside the particle locations. This extension provides an effective filtering of the OT solution beyond the local post-processing filters, as demonstrated by several numerical experiments. / Graduate

Some climate models are still lacking features such as dynamical modelling of ice sheets due to their computational cost which results in poor accuracy and estimates of e.g. sea level rise. The need for low-cost high-order models initiated the development of the First-Order Stokes (or Blatter-Pattyn) model which retains much of the accuracy of the full-Stokes model but is also cost-effective. This model has proven accurate for ice sheets and glaciers with frozen bedrocks, or no-slip basal boundary conditions. However, experimental evidence seems to be lacking regarding its accuracy under sliding, or stress-free, bedrock conditions (ice-shelf conditions). Hence, it became of interest to investigate this. Numerical experiments were set up by formulating the first-order Stokes equations as a variational finite element problem, followed by implementing them using the open-source FEniCS framework. Two types of geometries were used with both no-slip and slip basal boundary conditions. Specifically, experiments B and D from the Ice Sheet Model Intercomparison Project for Higher-Order ice sheet Models (ISMIP-HOM) were used to benchmark the model. Local model errors were investigated and a convergence analysis was performed for both experiments. The results yielded an inherent model error of about 0.06% for ISMIP-HOM B and 0.006% for ISMIPHOM D, mostly relating to the different types of geometries used. Errors in stress-free regions were greater and varied on the order of 1%. This was deemed fairly accurate, and probably enough justification to replace models such as the Shallow Shelf Approximation with the First-Order Stokes model in some regions. However, more rigorous tests with real-world geometries may be warranted. Also noteworthy were inconsistent results in the vertical velocity under slippery conditions (ISMIPHOM D) which could either be due to coding errors or an inherent problem with the decoupling of the horizontal and vertical velocities of the First-Order Stokes model. This should be further investigated. / Vissa klimatmodeller saknar fortfarande funktioner så som dynamisk modellering av istäcken på grund av dess höga beräkningskostnad, vilket resulterar låg noggrannhet och uppskattningar av t.ex. havsnivåhöjning. Behovet av enkla modeller med hög noggrannhet satte igång utvecklingen av den s.k. Första Ordningens Stokes (eller Blatter-Pattyn) modellen. Denna modell behåller mycket av noggrannheten i den mer exakta full-Stokes-modellen men är också väldigt kostnadseffektiv. Denna modell har visat sig vara noggrann för istäcken och glaciärer med frusna berggrunder eller s.k. no-slip randvillkor. Experimentella bevis tycks dock saknas med avseende på dess noggrannhet under glidning, eller stressfria, berggrundsförhållanden (t.ex. vid ishyllor). Därför ville vi undersöka detta. Numeriska experiment upprättades genom att formulera Blatter-Pattyn ekvatonerna som ett variationsproblem (via finita elementmetoden), följt av att implementera dem med hjälp av den öppna källkoden FEniCS. Två typer av geometrier användes med både glidande och stressfria basala randvillkor. Specifikt användes experiment B och D från Ice Sheet Model Intercomparison Project for Higher-Order ice sheet Models (ISMIP-HOM) för att testa modellen. Lokala fel undersöktes och en konvergensanalys utfördes för båda experimenten. Resultaten gav ett modellfel på ca 0,06 % för ISMIP-HOM B och 0,006 % för ISMIP-HOM D, vilka var mest relaterade till de olika typerna av geometrier som användes. Fel i stressfria regioner var större och varierade i storleksordningen 1 %. Detta ansågs vara ganska noggrant och sannolikt tillräckligt för att ersätta modeller så som Shallow Shelf Approximationen med Blatter-Pattyn-modellen i vissa regioner. Dock krävs mer noggranna tester med mer verkliga geometrier för att dra konkreta slutsatser. Också anmärkningsvärt var motsägande resultat i den vertikala hastigheten under glidande förhållanden (ISMIP-HOM D) som antingen kan ha berott på kodningsfel eller ett modelproblem som härstammar utifrån särkopplingen mellan den horizontella- och den vertikala hastigheten i Blatter-Pattyn-modellen. Detta bör undersökas vidare.

Neste trabalho, apresenta-se o resultado da existência de soluções fracas em domínios não-limitados para as equações de Navier-Stokes, desde que a fronteira satisfaça uma certa condição de regularidade que é necessária para a obtenção de estimativas em domínios não-limitados semelhantes à desigualdade de Poincaré em domínios limitados. Apresenta-se o desenvolvimento detalhado do método de Galerkin para as equações de Navier-Stokes em domínios não-limitados com cálculo explícito de várias constantes e com forças externas não nulas. Apresenta-se dois teoremas fundamentais: um fornecendo condições para existência de soluções do problema estacionário e o outro fornecendo condições para existência de soluções do problema não-estacionário. / In the work it is presented results of existence of weak solutions in unbounded doroains for the Navier-Stokes equations. The roain condition to obtain similar results as those for bounded doroains; for e."'Carople the Poincaré inequality; is a certain condition of regularity at the boundary of the doroain. It is presented the detailed developroent of the Galerkin roethod for the t.he Navier-Stokes equations in unbounded doroains ~vith the explicit calculat ions of many constants and ''rith non null externai forces. It is presented two basic theorern: one presenting condition for the existence of solutions for the stationary problem and the other presenting conditions for existence of solution for the non stationary problem.

A 3D parallel CFD code is written to investigate the characteristics of and differences between Large Eddy Simulation (LES) models in the context of simulating a thermal buoyant plume. An efficient multigrid scheme is incorporated to solve the Poisson equation, resulting from the fractional step, projection method used to solve the Low Mach Number (LMN) Navier-Stokes equations. A wide range of LES models are implemented, including a variety of eddy models, structure models, mixed models and dynamic models, for both the momentum stresses and the temperature fluxes. Generalised gradient flux models are adapted from their RANS counterparts, and also tested. A number of characteristics are observed in the LES models relating to the thermal plume simulation in particular and turbulence in general. Effects on transition, dissipation, backscatter, equation balances, intermittency and energy spectra are all considered, as are the impact of the governing equations, the discretisation scheme, and the effect of grid coarsening. Also characteristics to particular models are considered, including the subgrid kinetic energy for the one-equation models, and constant histories for dynamic models. The argument that choice of LES model is unimportant is shown to be incorrect as a general statement, and a recommendation for when the models are best used is given.