Details are given herein of the development, refinement and application of a higher-order accurate 3-D finite difference model for non-cohesive suspended sediment transport processes, in non-stratified estuarine and coastal waters. The velocity fields are computed using a 2-D horizontal depth-integrated model, in combination with either an assumed logarithmic velocity profile or a velocity profile obtained from field data. Also, for convenience in handling variable bed topographies and for better vertical resolution, a δ-stretching co-ordinate system has been used. In order to gain insight into the relative merits of various numerical schemes for modelling the convection of high concentration gradients, in terms of both accuracy and efficiency, thirty six existing finite difference schemes and two splitting techniques have been reviewed and compared by applying them to the following cases: i) 1-D and 2-D pure convection, ii) 1-D and 2-D convection and diffusion, and iii) 1-D non-linear Burger's equation. Modifications to some of the considered schemes have also been proposed, together with two new higher-order accurate finite difference schemes for modelling the convection of high concentration gradients. The schemes were derived using a piecewise cubic interpolation and an universal limiter (proposed scheme 1) or a modified form of the TVD filter (proposed scheme 2). The schemes have been tested for: i) 1-D and 2-D pure convection, and ii) 2-D convection and diffusion problems. The schemes have produced accurate, oscillation-free and non-clipped solutions, comparable with the ULTIMATE fifth- and sixth-order schemes. However, the proposed schemes need only three (proposed scheme 1) or five cell stencils. Hence, they are very attractive and can be easily implemented to solve convection dominated problems for complex bathymetries with flooding and drying. The 3-D sediment transport equation was solved using a splitting technique, with two different techniques being considered. With this technique the 3-D convective-diffusion equation for suspended sediment fluxes was split into consecutive 1-D convection, diffusion and convective-diffusion equations. The modified and proposed higher-order accurate finite difference schemes mentioned above were then used to solve the consecutive 1-D equations. The model has been calibrated and verified by applying it to predict the development of suspended sediment concentration profiles under non-equilibrium conditions in three test flumes. The results of numerical predictions were compared with existing analytical solutions and experimental data. The numerical results were in excellent agreement with the analytical solutions and were in reasonable agreement with the experimental data. Finally, the model has also been applied to predict sediment concentration and velocity profiles in the Humber Estuary, UK. Reasonable agreement was obtained between the model predictions and the corresponding field measurements, particularly when considered in the light of usual sediment transport predictions. The model is therefore thought to be a potentially useful tool for hydraulic engineers involved in practical case studies

The aerodynamics of modern rotorcraft is highly complex and has proven to be an arduous challenge for computational fluid dynamics (CFD). Flow features such as massively separated boundary layers or transition to turbulence are common in engineering applications and need to be accurately captured in order to predict the vehicle performance. The recent advances in numerical methods and turbulence modeling have resolved each of these issues independent of the other. First, state-of-the-art hybrid RANS-LES turbulence closures have shown great promise in capturing the unsteady flow details and integrated performance quantities for stalled flows. Similarly, the correlation-based transition model of Langtry and Menter has been successfully applied to a wide range of applications involving attached or mildly separated flows. However, there still lacks a unified approach that can tackle massively separated flows in the transitional flow region. In this effort, the two approaches have been combined and expended to yield a methodology capable of accurately predicting the features in these highly complex unsteady turbulent flows at a reasonable computational cost. Comparisons are evaluated on several cases, including a transitional flat plate, circular cylinder in crossflow and NACA 63-415 wing. Cost and accuracy correlations with URANS and prior hybrid URANS-LES approaches with and without transition modeling indicate that this new method can capture both separation and transition more accurately and cost effectively. This new turbulence approach has been applied to the study of wings in the reverse flow regime. The flight envelope of modern helicopters has increased significantly over the last few decades, with design concepts now reaching advance ratios up to μ = 1. In these extreme conditions, the freestream velocity exceeds the rotational speed of the blades, and a large region of the retreating side of the rotor disk experiences reverse flow. For a conventional airfoil with a sharp trailing edge, the reverse flow regime is generally characterized by massive boundary layer separation and bluff body vortex shedding. This complex aerodynamic environment has been utilized to evaluate the new hybrid transitional approach. The assessment has proven the efficiency of the new hybrid model, and it has provided a transformative advancement to the modeling of dynamic stall.

Computing reliable numerical approximations of invariant sets for nonlinear systems is the core problem for computer assisted study of dynamical systems. In the case of conservative systems the problem is complicated by the fact that there is no phase space dissipation to drive orbits onto attractors. In this dissertation we discuss several contributions to the field of computer assisted study of invariant dynamics in conservative systems. / text

A numerical reservoir model was created to optimize CO₂ Huff-and-Puff operations in the Bakken Shale. Huff-and-Puff is an enhanced oil recovery treatment in which a well alternates between injection, soaking, and production. Injecting CO₂ into the formation and allowing it to “soak” re-pressurizes the reservoir and improves oil mobility, boosting production from the well. A compositional reservoir simulator was used to study the various design components of the Huff-and-Puff process in order to identify the parameters with the largest impact on recovery and understand the reservoir’s response to cyclical CO₂ injection. It was found that starting Huff-and-Puff too early in the life of the well diminishes its effectiveness, and that shorter soaking periods are preferable over longer waiting times. Huff-and-Puff works best in reservoirs with highly-conductive natural fracture networks, which allow CO₂ to migrate deep into the formation and mix with the reservoir fluids. The discretization of the computational domain has a large impact on the simulation results, with coarser gridding corresponding to larger projected recoveries. Doubling the number of hydraulic fractures per stage results in considerably greater CO₂ injection requirements without proportionally larger incremental recovery factors. Incremental recovery from CO₂ Huff-and-Puff appears to be insufficient to make the process commercially feasible under current economic conditions. However, re-injecting mixtures of CO₂ and produced hydrocarbon gases was proven to be technically and economically viable, which could significantly improve profit margins of Huff-and-Puff operations. A substantial portion of this project involved studying alternative numerical methods for modeling hydraulically-fractured reservoir models. A domain decomposition technique known as mortar coupling was used to model the reservoir system as two individually-solved subdomains: fracture and matrix. A mortar-based numerical reservoir simulator was developed and its results compared to a tradition full-domain finite difference model for the Cinco-Ley et al. (1978) finite-conductivity vertical fracture problem. Despite some numerical issues, mortar coupling closely matched Cinco-Ley et al.'s (1978) solution and has potential applications in complex problems where decoupling the fracture-matrix system might be advantageous. / text

This thesis consists of four papers that concern error estimates for the Born-Oppenheimer molecular dynamics, and adaptive algorithms for the Car-Parrinello and Ehrenfest molecular dynamics. In Paper I, we study error estimates for the Born-Oppenheimer molecular dynamics with nearly crossing potential surfaces. The paper first proves an error estimate showing that the difference of the values of observables for the time-independent Schrödinger equation, with matrix valued potentials, and the values of observables for the ab initio Born-Oppenheimer molecular dynamics of the ground state depends on the probability to be in the excited states and the nuclei/electron mass ratio. Then we present a numerical method to determine the probability to be in the excited states, based on the Ehrenfest molecular dynamics, and stability analysis of a perturbed eigenvalue problem. In Paper II, we present an approach, motivated by the so called Landau-Zener probability estimation, to systematically choose the artificial electron mass parameters appearing in the Car-Parrinello and Ehrenfest molecular dynamics methods to approximate the Born-Oppenheimer molecular dynamics solutions. In Paper III, we extend the work presented in Paper II for a set of more general problems with more than two electron states. A main conclusion of Paper III is that it is necessary to resolve the near avoided conical intersections between all electron eigenvalue gaps, including gaps between the occupied states. In Paper IV, we numerically compare, using simple model problems, the Ehrenfest molecular dynamics using the adaptive mass algorithm proposed in Paper II and III and the Born-Oppenheimer molecular dynamics based on the so called purification of the density matrix method concluding that the Born-Oppenheimer molecular dynamics based on purification of density matrix method performed better in terms of computational efficiency. / <p>QC 20161102</p>

Stability analysis methods may be categorized by two major stability analysis methods: small-signal stability and transient stability analyses. Transient stability methods are further categorized into two major categories: numerical methods based on numerical integration, and direct methods. The purpose of this thesis is to study and investigate transient stability analysis using a combination of step-by-step and direct methods using Equal Area Criterion. The proposed method is extended for transient stability analysis of multi machine power systems. The proposed method calculates the potential and kinetic energies for all machines in a power system and then compares the largest group of kinetic energies to the smallest groups of potential energies. A decision based on the comparison can be made to determine stability of the power system. The proposed method is used to simulate the IEEE 39 Bus system to verify its effectiveness by comparison to the results obtained by pure numerical methods.

<div>A strongly implicit, nonlinear Crank-Nicolson-based finite-difference scheme was constructed for the numerical study of the self-similar behavior of viscous gravity currents. Viscous gravity currents are low Reynolds number flow phenomena in which a dense, viscous fluid displaces a lighter (usually immiscible) fluid. Under the lubrication approximation, the mathematical description of the spreading of these fluids is reduced to solving a nonlinear parabolic partial differential equation for the shape of the fluid interface. This thesis focuses on the finite-speed propagation of a power-law non-Newtonian current in a variable width channel-like geometry (a "Hele-Shaw cell'') subject to a given mass conservation/balance constraint. The proposed numerical scheme was implemented on a uniform but staggered grid. It is shown to be strongly stable, while possessing formal truncation error that is of second-order in space and it time. The accuracy of the scheme was verified by benchmarking it against established analytical solutions, which were obtained via a first-kind self-similarity transformation. A series of numerical simulations confirmed that the proposed scheme accurately respects the mass conservation/balance constraint. Next, the numerical scheme was used to study the second-kind self-similar behaviour of Newtonian viscous gravity currents flowing towards the end of a converging channel. Second-kind self-similar transformations are not fully specified without further information from simulation or experiment. Thus, using the proposed numerical scheme, the self-similar spreading and leveling leveling of the current was definitively addressed. The numerical results showed favorable comparison with experimental data.</div>

ESS neutrino Super Beam (ESSnuSB) is a project that aim to create ahigh energy beam of neutrinos and anti-neutrinos to study thephenomenon neutrino oscillation and learn more about symmetryviolations in quantum mechanics. To create the neutrino beam, negativeHydrogen ions must be transported from the ESS linear accelerator at2.5 GeV, to a proton accumulation ring. This is done through a transferline, that shall direct the ion beam while preserve the beam as much aspossible. In thisproject, there was an attempt at finding a design for this transferline. Preferably, the line consists of a long main line of FODO cellsand two matching sections at each end. A simulation of the beam wasdone that gives the progression beta and dispersion functions,statistical measurements of the particle distribution, through a partof the transfer line. A design for the main line was found. For tuningthe quadrupole magnets, an iterative method using the system's responsematrix was used. However, it could not match more than four parametersat the time, while six was required for complete matching. Because ofthis, it is not able to match thedispersion.

Um mecanismo móvel instalado no interior de tanques, e conectado à estrutura por molas é proposto para atenuar os efeitos de sloshing em diferentes níveis de preenchimento. Para realizar o estudo e desenvolvimento deste dispositivo, foram propostas duas ferramentas de análise. A primeira ferramenta é baseada em uma formulação desenvolvida analiticamente que calcula a resposta das forças nas paredes do tanque no domínio da frequência. Esta formulação foi desenvolvida como um sistema mecânico de dois graus de liberdade, onde são representados o corpo móvel e o sloshing descrito como um sistema do tipo massa-mola. A segunda ferramenta é uma abordagem utilizando simulações numéricas baseada em um método de partículas de cálculo de escoamento. O método numérico utilizado foi o Moving Particle Semi-implicit (MPS) que calcula o comportamento do fluido interagindo com o corpo móvel e as paredes do tanque sem restrições de movimento. Resultados qualitativos do método analítico foram analisados e mostraram-se bastante consistentes. Resultados quantitativos dos métodos analíticos e numéricos foram comparados com os resultados presentes na literatura e entre si com uma boa concordância. O método analítico é eficiente no dimensionamento inicial do corpo móvel considerando apenas efeitos lineares, e o método numérico é mais indicado para análises mais detalhadas onde efeitos não-lineares podem ser considerados. A integração dos efeitos do corpo móvel no sloshing mostra que o dispositivo de supressão é eficaz em diferentes razões de preenchimento do tanque na atenuação dos efeitos gerados pelo sloshing. / A movable mechanism installed inside tanks and connected to the structure by springs is proposed to attenuate the sloshing effects for different filling ratios. To carry on the investigation and the development of this device, two analysis approaches were elaborated. The first approach is based on an analytical formulation that describes the coupled motion calculating the sloshing force on the walls in the frequency domain. This formulation was developed as a mechanical system with two degrees of freedom representing the moving body and the sloshing described as a mass-spring system. The second tool is an approach that uses numerical simulations based on a particle method to calculate the fluid flow called Moving Particle Semi- implicit method (MPS). This numerical approach calculates the fluid behavior interacting with the moving body and the tank walls without motions restrictions. Qualitative results of the analytical method were analyzed and they were consistent. Quantitative results of the analytical and numerical approaches were compared with the results found in the literature with good agreement. The analytical method is useful to define the moving device initial design considering only linear effects, and the numerical approach is indicated to more detailed analysis where non-linear effects can take place. The integration of the effects of sloshing with the moving body shows the effectiveness of the device for different filling ratios to attenuate the sloshing loads.

A simulação de escoamentos com superfícies livres vem ganhando importância ao longo dos últimos anos devido às várias aplicações práticas em que esse tipo de escoamento está envolvido. Dentre os métodos numéricos existentes para a simulação de escoamentos, temos o GENSMAC, que é uma técnica numérica para simular escoamentos newtonianos com superfícies livres. A implementação de métodos semi-implícitos para a discretização temporal das equações de Navier-Stokes permitiu uma relaxação significativa na restrição no passo temporal, reduzindo consideravelmente o custo computacional na simulação de escoamentos com Re 1. Mas, mesmo no caso dos métodos semi-implícitos, o passo temporal não pode aumentar além de certos limites, bem aquém daquele da restrição CFL, sem provocar sérios problemas de precisão nos resultados numéricos e consequente aparecimento de resultados não físicos. Portanto, mesmo na formulação semi-implícita, uma restrição no passo temporal é aplicada. Neste trabalho, analisamos e implementamos no sistema FREEFLOW2D uma estratégia de adaptação do passo temporal de maneira a garantir a estabilidade e a precisão utilizando o maior passo temporal possível. A eficiência e robustez da técnica incorporada à formulação implícita do GENSMAC são demonstradas na solução de problemas bidimensionais complexos com superfícies livres e baixo número de Reynolds, incluindo os problemas do inchamento do extrudado e jet flow / The simulation of free surfaces flows has gained importance in the recent years due to the many practical applications of this type of flow. Among the many numerical methods available for the simulation of fluid flows, there is GENSMAC, which is a numerical technique to simulate Newtonian flows with free surfaces. The implementation of semi-implicitmethods for the temporal discretization of the Navier-Stokes equations allowed a significant loosening in the time step restriction, reducing considerably the computational cost of the simulation of flows with Re 1. But, even with the semi-implicit methods, the time step cannot increase beyond certain limits, well below the CFL restriction, without causing serious accuracy problems in the numerical results and the consequent appearance of non-physical results. Therefore, even in the semi-implicit formulation, a time step restriction is applied. In this work, we analyse and implement in the FREEFLOW2D system a strategy for adaptive time-stepping in order to ensure stability and precision while using the largest possible time step. The efficiency and robustness of the technique incorporated to the implicit formulation of GENSMAC are demonstrated in the solution of two-dimensional complex problems with free surfaces and low Reynolds numbers, including the swelling of the extrudate and jet flow problems