Neste projeto, é apresentado um método numérico com uma abordagem do tipoMAC para a simulação de escoamentos viscoelásticos incompressíveis tridimensionais com superfície livre governados pelo modelo de fluido SXPP. A formulação apresentada nesse trabalho é uma extensão dos resultados obtidos por Oishi et al. (2011), sobre o estudo de métodos numéricos para a simulação de escoamentos incompressíveis viscoelásticos com superfície livre a baixos números de Reynolds, para o caso bidimensional. No contexto de problemas transientes, metodologias explícitas para solução numérica das equações governantes apresentam restrições de estabilidade muito severas para a definição do passo temporal, acarretando em um custo computacional relativamente alto. Sendo assim, utilizamos um método implícito para resolver a equação de conservação da quantidade de movimento, eliminando assim, a restrição de estabilidade parabólica e diminuindo significativamente o custo computacional. Mas tal estratégia acopla os campos de velocidade e pressão. Dessa forma, para desacoplar esses campos, foi utilizado uma abordagem que combina método de projeção com uma técnica implícita para o tratamento da pressão na superfície livre. A equação constitutiva foi resolvida pelo método de Runge-Kutta de segunda-ordem. A validação do método numérico foi realizada utilizando refinamento da malha no escoamento em um canal. Como aplicação, apresentamos resultados numéricos sobre o problema do jato oscilante e do inchamento do extrudado / In this work, we present a numerical method with a MAC type approach to simulate tridimensional incompressible viscoelastic free surface flows governed by a SXPP (Single eXtended Pom-Pom) model. The formulation presented in this work is an extension to the work of Oishi et al. (2011). They have studied numerical methods for solving incompressible viscoelastic free surface flows with low Reynolds number, for the bidimensional case. In the context of transient problems, explicitmethodologies for the numerical solution of the governing equations present severe stability constraints for defining the time step, what highly increases the computational cost. Due to this fact, an implicit method is used to solve the momentum equation, eliminating the parabolic stability constraint and decreasing significantly the computational cost. However, this strategy couples velocity and pressure fields. To decouples this fields, it was used an approach that combines a projection method and an implicit technique for the treatment of the pressure at the free surface. The constitutive equation is solved by a second-order Runge-Kutta method. The numerical method validation was achieved by a mesh refinement for a flow in a channel. As applications, numerical results of the die-swell problem and the jet buckling phenomenon are presented

>Magister Scientiae - MSc / This thesis deals with analysis and implementation of a positivity preserving numerical method for a vaccination model for the transmission dynamics of two HIVsubtypes in a given community. The continuous model is analyzed for stability and equilibria. The qualitative information thus obtained is used while designing numerical method(s). Three numerical methods, namely, Implicit Finite Difference Method (IFDM), Non-standard Finite Difference Method (NSFDM) and the Runge-Kutta method of order four (RK4), are designed and implemented. Extensive numerical simulation are carried out to justify theoretical outcomes.

The steady flow method (SFM), most commonly used for permeability measurement in the laboratory, is not applicable for tight rocks, higher rank coals and coals under highly stressed condition because of the difficulty in measuring steady-state gas flowrates resulting from the tight rock structure of. However, accurate estimation of permeability of highly stressed coals is pivotal in coalbed methane (CBM) operations in order to precisely and effectively model and project long-term gas production. A fast and accurate permeability measurement technique is, therefore, required to investigate gas flow behavior of CBM reservoirs. The pulse-decay method (PDM) of permeability measurement is believed to be better suited for low-permeability rocks. In this study, application of the currently used pulse-decay laboratory permeability measurement techniques for highly stressed coals were evaluated. Considering the limitations of these techniques in permeability measurement of unconventional gas reservoirs, such as coal and gas shales, the conventional PDM was optimized by adjusting the experimental apparatus and procedures. Furthermore, the applicability of an optimized PDM was verified numerically and experimentally. This dissertation is composed of five chapters. To complete the research objectives as discussed above, it is necessary to have a profound understanding of the basic theories, such as, gas storage mechanism, gas migration, and permeability evolution during gas depletion in coalbed reservoirs. In Chapter 1, a brief discussion regarding the basic knowledge of reservoir properties and transport mechanisms is presented. The chapter also provides the appropriate background and rationale for the theoretical and experimental work conducted in this study. Chapter 2 presents the transient pressure-decay technique in permeability measurement of highly stressed coals and verifies the validity of Brace et al.’s solution (1968) by comparing it with Dicker and Smits’s solution (1988) and Cui et al.’s solution. The differences between these three solutions are discussed in detail. Based on the established permeability trends from these different solutions, a persuasive suggestion is presented for selection of the best alternative when testing coal permeability. Furthermore, permeability is regarded as a coupled parameter, resulting from the combined effects of mechanical compression and “matrix shrinkage” caused by desorption of gas. To isolate the role of gas desorption from the coupled result, a series of experiments were carried out under constant effective stress condition and a stress-dependent permeability trend was established. Chapter 3 proposes an optimized experimental design in order to improve the accuracy of the calculated permeability for sorptive rocks. In order to verify the optimized design theoretically, a modified mathematical model is presented and describes the one-dimensional fluid flow in porous media by a partial differential equation. The numerical solutions of the model are presented graphically to evaluate the fluid flow behavior in porous media. Finally, the validity of Brace et al.’s solution when testing sorptive rocks, without the need of consideration on the compressive storage and sorption effect, is elucidated. Chapter 4 demonstrates the efficiency and applicability of the optimized PDM through its direct application to experimental work designed to establish the permeability trend under best replicated in situ conditions. In this chapter, CO2 was used as the test fluid to profile and characterize the pulse decay plots due to its higher affinity towards coal than methane, and then establish the stress-dependent-permeability trend for highly-stressed CBM reservoirs. In this chapter, Brace et al.’s solution was also verified by comparing the laboratory data and computer simulated results obtained from the optimized mathematical model proposed in Chapter 3. The experimental work demonstrates that the optimized technique can be used for permeability tests of sorptive rocks without the need to carry out additional experimental work required to measure rock porosities and sorption isotherms. Finally, a summary and future research perspectives are presented in Chapter 5.

No abstract is provided. / Thesis / Master of Engineering (MEngr) / Scope and contents: The aim of this thesis is to present a finite difference method, for analysing coupled shear walls with constant or variable cross-section, resting on rigid or elastic foundations and with elastic or inelastic connecting beams. It is also intended to compare the finite difference method with the continuous connection method, which can be developed using Rosman's approach or Newmark's concept for analysing composite beams or the energy approach, and with the finite element method. An analysis of coupled shear walls with multiple piers is presented.

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No / This paper presents an investigation into the impact of data dependencies in real-time high performance sequential and parallel processing. An adaptive active vibration control algorithm is considered to demonstrate the impact of data dependencies in real-time computing. The algorithm is analysed in detail to explore the inherent data dependencies. To minimize the impact of data dependencies, an investigation into reducing memory access in sequential computing is provided. The impact of data dependencies with various interconnections is also explored and demonstrated in real-time parallel processing through a set of experiments.

Today, heterogeneous computing has truly reshaped the way scientists think and approach high-performance computing (HPC). Hardware accelerators such as general-purpose graphics processing units (GPUs) and Intel Many Integrated Core (MIC) architecture continue to make in-roads in accelerating large-scale scientific applications. These advancements, however, introduce new sets of challenges to the scientific community such as: selection of best processor for an application, effective performance optimization strategies, maintaining performance portability across architectures etc. In this thesis, we present our techniques and approach to address some of these significant issues. Firstly, we present a fully automated approach to project the relative performance of an OpenCL program over different GPUs. Performance projections can be made within a small amount of time, and the projection overhead stays relatively constant with the input data size. As a result, the technique can help runtime tools make dynamic decisions about which GPU would run faster for a given kernel. Usage cases of this technique include scheduling or migrating GPU workloads over a heterogeneous cluster with different types of GPUs. We then present our approach to accelerate a seismology modeling application that is based on the finite difference method (FDM), using MPI and CUDA over a hybrid CPU+GPU cluster. We describe the generic computational complexities involved in porting such applications to the GPUs and present our strategy of efficient performance optimization and characterization. We also show how performance modeling can be used to reason and drive the hardware-specific optimizations on the GPU. The performance evaluation of our approach delivers a maximum speedup of 23-fold with a single GPU and 33-fold with dual GPUs per node over the serial version of the application, which in turn results in a many-fold speedup when coupled with the MPI distribution of the computation across the cluster. We also study the efficacy of GPU-integrated MPI, with MPI-ACC as an example implementation, in a seismology modeling application and discuss the lessons learned. / Master of Science