Tsunamis are one of the most catastrophic natural events impacting coastal regions often generated by undersea earthquakes. Nevertheless, in enclosed basins, i.e., fjords, reservoirs and lakes, subaerial or submarine landslides can initiate devastating tsunamis with similar consequences. Although a subaerial or submarine landslide that impinges into a large water body can generate a tsunami, subaerial landslides are much more efficient tsunami generators than its counterpart. In this study we aim to integrate laboratory scale experiments of tsunami generation by subaerial landslide with numerical models. The work focuses on the numerical validation of two three-dimensional Navier-Stokes (3D-NS) models, FLOW-3D and our developed model TSUNAMI3D. The models are validated based on previous large scale laboratory experiments performed by a tsunami research team lead by Dr. Hermann Fritz, Georgia Institute of Technology. Three large scale landslide scenarios were selected from the set of laboratory experiments, namely, fjord like, headland and far field coastline. These scenarios showed that complex wave fields can be generated by subaerial landslides. The correct definition and evolution of the wave field are key to accurate modeling the ensuing tsunami and its effect in coastal regions. In this study, comparisons are performed between numerical results and laboratory experiments. Methodology and key parameters for soil rheology are defined for model validations. Results of the models are expected to be under the allowable errors indicated by the National Tsunami Hazard Mitigation Program (NTHMP), National Oceanic and Atmospheric Administration (NOAA) guidelines for validation of tsunami numerical models. The ultimate goal of this research is to obtain better tsunami calculation tools for real-world application of 3-D models for landslide tsunamis, which are necessary for the construction of inundation maps in the Gulf of Mexico and the Caribbean regions.

Fluid simulating is one of the most difficult problems in computer graphics. On the other hand, water appears in our life very frequently. This thesis focuses on water simulating. We have two main methods to do this in the thesis: the first is wave based water simulating; Sine wave summing based and Fast Fourier Transform based methods are all belong to this part. The other one is physics based water simulating. We make it based on Navier-Stokes Equation and it is the most realistic animation of water. It can deal with the boundary and spray which other method cannot express. Then we put our emphasis on implement by the physics method using Navier-Stokes Equation.

A simulação numérica de escoamentos de fluidos em uma grande variedade de aplicações requer a utilização de técnicas numéricas de alta eficência e recursos computacionais de alto desempenho. O objetivo deste trabalho é iniciar uma investigação de escoamentos de fluido durante o enchimento de compartimentos de reservatórios. Uma abordagem inicial foi tratar problemas de escoamento em um canal, rebuscando a geometria do domínio para contemplar problemas mais complexos. Este trabalho apresenta o desenvolvimento e os resultados obtidos de um método numérico para simulação de escoamento de fluido incompressível em um domínio tridimensional, onde as equações de Navier-Stokes são desenvolvidas em uma formulação euleriana e discretizadas pelo método de elementos finitos. Os termos convectivos destas equações foram tratados pelo método semi-lagrangeano e o método de Galerkin foi utilizado para discretização espacial, um método baseado em decomposição LU foi utilizado para desacoplar as componentes de velocidade e pressão, sendo esta última calculada utilizando-se uma aproximação hidrostática. O domínio tridimensional foi representado por uma malha manipulada por uma estrutura de dados topológica, formada por células que definem elementos prismáticos lineares. Foram realizados experimentos sob várias alterações na geometria do domínio e também sob diferentes condições iniciais. Os resultados mostraram uma boa aproximação do método, quando analisado comparativamente a uma solução analítica / The numerical simulation of fluid flow over many applications require the use of numerical techniques of high efficiency and demand high computational power. This work aims at initiating an investigation about fluid flows while filling reservoirs. The initial approach was to deal with fluid flows in a retangular duct, as increasing the complexity of its geometry in order to model more complex cases. This document describes the development of a numerical method for the simulation of incompressible fluid flow over a threedimentional domain, where the Navier-Stokes equations were written under an Eulerian formulation and discretized by the Finite Elements Method. The semi-Lagrangean method was used to discretize the convective terms and the components of velocity and pressure were decoupled through the use of a method based on LU decomposition, where the final pressure was determined by using a hidrostatic aproximation. The threedimentional domain was represented by a mesh, manipulated by a topologic data structure, formed with cells that define linear prismatic elements. Many experiments were performed under different geometries of the domain and also under different initial conditions. The result showed a good approximation of the described method, when compared with an analitical solution

The study of finite-sized, deformable droplets adverted by turbulent flows is an active area of research. It spans many streams of sciences and engineering, which include chemical engineering, fluid mechanics, statistical physics, nonlinear dynamics, and also biology. Advances in experimental techniques and high-performance computing have made it possible to investigate the properties of turbulent fluids laden with droplets. The main focus of this thesis is to study the statistical properties of the dynamics of such finite-size droplets in turbulent flows by using direct numerical simulations (DNSs). The most important feature of the model we use is that the droplets have a back-reaction on the advecting fluid: the turbulent fluid affects the droplets and they, in turn, affect the turbulence of the fluid. Our study uncovers (a) statistical properties that characterize the spatiotemporal evolution of droplets in turbulent flows, which are statistically homogeneous and isotropic, and (b) the modification of the statistical properties of this turbulence by the droplets. This thesis is divided into seven Chapters. Chapter 1 contains an introduction to the background material that is required for this thesis, especially the details about the equations we use; it also contains an outline of the problems we study in subsequent Chapters. Chapter 2 contains our study of “Droplets in Statistically Homogeneous Turbulence: From Many Droplets to a few Droplets”. Chapter 3 is devoted to our study of “Coalescence of Two Droplets”. Chapter 4 deals with “Binary-Fluid Turbulence: Signatures of Multifractal Droplet Dynamics and Dissipation Reduction”. Chapter 5 deals with “A BKM-type theorem and associated computations of solutions of the three-dimensional Cahn-Hilliard-Navier-Stokes equations”. Chapter 6 is devoted to our study of “Turbulence-induced Suppression of Phase Separation in Binary-Fluid Mixtures”. Chapter 7 is devoted to our study of “Antibubbles: Insights from the Cahn-Hilliard-Navier-Stokes Equations”.

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This thesis deals with the Navier-Stokes equations for real, compressible fluid with first and second viscosity. The method of expansion into a series of eigenmodes of vibration is chosen to solve the Navier-Stokes equations. The general relations of the expansion coefficients and the eigenmode shapes are given for 1D-, 2D- and 3D-flows. The specific formulae of eigenmodes of vibration are determined only for 1D-flow. The final form of the pressure function is analysed using Matlab software.

We examine the Rayleigh–Bénard convection as modelled by the Boussinesq equation. Our aim is at deriving bounds for the heat enhancement factor in the vertical direction, the Nusselt number, which reproduce physical scalings. In the first part of the dissertation, we examine the the simpler model when the acceleration of the fluid is neglected (Pr=∞) and prove the non-optimality of the temperature background field method by showing a lower bound for the Nusselt number associated to it. In the second part we consider the full model (Pr<∞) and we prove a new upper bound which improve the existing ones (for large Pr numbers) and catches a transition at Pr~Ra^(1/3).

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