>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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A one-dimensional model of a heterogeneous material consisting of a matrix with embedded separated particles is considered, and the melting or solidification of the particles is investigated. The matrix is in imperfect contact with the particles, and the lumped capacity approximation applies to each individual particle. Heat is generated inside the particles or is transferred from the matrix to the particles coupled through a contact conductance. The matrix is not allowed to change phase and energy is either generated inside the matrix or transferred from the boundaries, which is initially conducted through the matrix material. The physical model of this coupled, two-step heat transfer process is solved using the energy method. The investigation is conducted in several phases using a building block approach. First, a lumped capacity system during phase transition is studied, then a one-dimensional homogeneous material during phase change is investigated, and finally the one-dimensional heterogeneous material is analyzed. A numerical solution based on the finite difference method is used to solve the model equations. This method allows for any kind of boundary conditions, any combination of material properties, particle sizes and contact conductance. In addition, computer programs, using Mathematica, are developed for the lumped capacity system, homogeneous material, and heterogeneous material. Results show the effects of control volume thickness, time step, contact conductance, material properties, internal sources, and external sources. / Master of Science

For realistic predictions of vehicle performance in off-road conditions, it is critical to incorporate in the simulation accurate representations of the variability of the terrain profile. It is not practically feasible to measure the terrain at a sufficiently large number of points, or, if measured, to use such data directly in the simulation. Dedicated modeling techniques and computational methods that realistically and efficiently simulate off-road operating conditions are thus necessary. Many studies have been recently conducted to identify effective and appropriate ways to reduce experimental data in order to preserve only essential information needed to re-create the main terrain characteristics, for future use. This thesis focuses on modeling terrain profiles using the finite difference approach for solving linear second-order stochastic partial differential equations. We currently use this approach to model non-stationary terrain profiles in two dimensions (i.e., surface maps). Certain assumptions are made for the values of the model coefficients to obtain the terrain profile through the fast computational approach described, while preserving the stochastic properties of the original terrain topology. The technique developed is illustrated to recreate the stochastic properties of a sample of terrain profile measured experimentally. To further analyze off-road conditions, stochastic soil properties are incorporated into the terrain topology. Soil models can be developed empirically by measuring soil data at several points, or they can be created by using mathematical relations such as the Bekker's pressure-sinkage equation for homogeneous soils. In this thesis, based on a previously developed stochastic soil model, the polynomial chaos method is incorporated in the soil model. In a virtual proving ground, the wheel and soil interaction has to be simulated in order to analyze vehicle maneuverability over different soil types. Simulations have been created on a surface map for different case studies: stepping with a rigid plate, rigid wheel and flexible wheel, and rolling of a rigid wheel and flexible wheel. These case studies had various combinations of stochastic or deterministic terrain profile, stochastic or deterministic soil model, and an object to run across the surface (e.g., deterministic terrain profile, stochastic soil model, rolling rigid wheel). This thesis develops a comprehensive terrain and soil simulation environment for off-road mobility studies. Moreover, the technique developed to simulate stochastic terrain profile can be employed to simulate other stochastic systems modeled by PDEs. / Master of Science

京都大学 / 新制・課程博士 / 博士(工学) / 甲第25262号 / 工博第5221号 / 新制||工||1996(附属図書館) / 京都大学大学院工学研究科都市社会工学専攻 / (主査)教授 岸田 潔, 教授 安原 英明, 准教授 橋本 涼太 / 学位規則第4条第1項該当 / Doctor of Agricultural Science / Kyoto University / DFAM