Slip on the geometrically complex Rhyolite Ridge Fault System and associated local stresses in the Desert Peak Geothermal Field in Nevada, were modeled with the boundary element method (BEM) implemented in Poly3D. The impact of uncertainty in the fault geometry at depth, the tectonic stresses driving slip, and the potential ranges of frictional strength resisting slip on the likely predictions of fracture slip and formation in the surrounding volume due to these local stresses were systematically explored and quantified. The effect of parameter uncertainty was evaluated by determining the frequency distribution of model predicted values. Alternatively, Bayesian statistics were used to determine the best fitting values for parameters within a probability distribution derived from the difference of the model prediction from the observed data. This approach honors the relative contribution of uncertainties from all existing data that constrains the fault parameters. Lastly, conceptual models for different fault geometries and their evolution were heuristically explored and the predictions of local stress states were compared to available measurements of the local stresses, fault and fracture patterns at the surface and in boreholes, and the spatial extent of the geothermal field. The complex fault geometry leads to a high degree of variability in the locations experiencing stress states that promote fracture, but such locations generally correlate with the main injection and production wells at Desert Peak. In addition, the strongest and most common stress concentrations occur within relays between unconnected fault segments, and at bends and intersections in faults that connect overlapping fault segments associated with relays. The modeling approach in this study tests the conceptual model of the fault geometry at Desert Peak while honoring mechanical constants and available constraints on driving stresses and provides a framework that aids in geothermal exploration by predicting the spatial variations in stresses likely to cause and reactivate fractures necessary to sustain hydrothermal fluid flow. This approach also quantifies the relative sensitivity of such predictions to fault geometry, remote stress, and friction, and determines the best fitting model with its associated probability. / Geology

Melting and vaporization of solids occur very often in nature and in man-made processes. Many analytical and numerical solutions exist for solving the temperature field in the liquid and solid regions, but inaccuracies persist in tracking the phase change interfaces and the numerical solution of the temperature field is usually cumbersome. The Boundary Element Method is proposed as an accurate, efficient way to solve for the temperature field and the interface positions in a phase change problem involving combined melting and vaporization. When comparing to specific one-dimensional test cases, accurate results arc obtained when using a sufficiently small time step. A comparison is made to existing data from a laser drilling experiment. The anticipated physical effects which occur on semi-infinite and finite domains arc confirmed. Consequently, this method can be used to model natural and industrial phenomena involving phase change. / Master of Science

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This work presents detailed numerical calculations of the dielectrophoretic force in octupolar traps designed for single-cell trapping. A trap with eight planar electrodes is studied for spherical and ellipsoidal particles using an indirect implementation of the boundary element method (BEM). Multipolar approximations of orders one to three are compared with the full Maxwell stress tensor (MST) calculation of the electrical force on spherical particles. Ellipsoidal particles are also studied, but in their case only the dipolar approximation is available for comparison with the MST solution. The results show that the full MST calculation is only required in the study of non-spherical particles. / Singapore-MIT Alliance (SMA)

In this study, a heterogeneous flow model is proposed based on a non-overlapping domain decomposition method. The model combines potential flow and incompressible viscous flow. Both flow domains contain a free surface boundary. The heterogeneous domain decomposition method is formulated following the Dirichlet-Neumann method. Both an implicit scheme and an explicit scheme are proposed. The algebraic form of the implicit scheme is of the same form of the Dirichlet--Neumann method, whereas the explicit scheme can be interpreted as the classical staggered scheme using the splitting of the Dirichlet-Neumann method. The explicit scheme is implemented based on two numerical solvers, a Boundary element method (BEM) solver for the potential flow model, and a finite element method (FEM) solver for the Navier-Stokes equations (NSE). The implementation based on the two solvers is validated using numerical examples. / Graduation date: 2013

No contexto do método dos elementos de contorno, este trabalho apresenta comparativamente três formulações em distintos aspectos. Visando a análise de sólidos bidimensionais no campo da mecânica da fratura, primeiramente é estudada a equação singular ou em deslocamentos. Em seguida, a formulação hiper-singular ou em forças de superfície é avaliada. Por último, a formulação dual, que emprega ambas equações é analisada. Para esta análise, elementos contínuos e descontínuos são empregados, equações numéricas e analíticas com ponto fonte dentro e fora do contorno são testadas, usando aproximação linear. A formulação é inicialmente empregada a problemas da mecânica da fratura elástica linear e em seguida extendida a problemas não-lineares, especialmente o modelo coesivo. Exemplos numéricos diversos averiguam as formulações, comparando com resultados analíticos ou disponíveis na literatura. / In this work three boundary elment formulations applied to fracture mechanics are studied. Aiming the analysis of two-dimensional solids with emphasis on the crack problem, the first considered method is the one based on using displacement equations only (singular formulation). The second scheme discussed in this work is a formulation based on the use of traction equations (hyper-singular formulation). Finally the dual boundary element method that uses singular and hyper-singular equations is considered. The numerical schemes have been implemented using continuous and discontinuous linear boundary and crack elements. The boundary and crack integral were all carried out by using analytical expressions, therefore increasing the accuracy of the algebraic system obtained for each one of the studied schemes. The developed numerical programs were applied initially to elastic fracture mechanics and then extended to analyze cohesive cracks. Several numerical examples were solved to verify the accuracy of each one of the studied models, comparing the results with the analytical solutions avaliable in the literature.

No contexto do método dos elementos de contorno, este trabalho apresenta comparativamente três formulações em distintos aspectos. Visando a análise de sólidos bidimensionais no campo da mecânica da fratura, primeiramente é estudada a equação singular ou em deslocamentos. Em seguida, a formulação hiper-singular ou em forças de superfície é avaliada. Por último, a formulação dual, que emprega ambas equações é analisada. Para esta análise, elementos contínuos e descontínuos são empregados, equações numéricas e analíticas com ponto fonte dentro e fora do contorno são testadas, usando aproximação linear. A formulação é inicialmente empregada a problemas da mecânica da fratura elástica linear e em seguida extendida a problemas não-lineares, especialmente o modelo coesivo. Exemplos numéricos diversos averiguam as formulações, comparando com resultados analíticos ou disponíveis na literatura. / In this work three boundary elment formulations applied to fracture mechanics are studied. Aiming the analysis of two-dimensional solids with emphasis on the crack problem, the first considered method is the one based on using displacement equations only (singular formulation). The second scheme discussed in this work is a formulation based on the use of traction equations (hyper-singular formulation). Finally the dual boundary element method that uses singular and hyper-singular equations is considered. The numerical schemes have been implemented using continuous and discontinuous linear boundary and crack elements. The boundary and crack integral were all carried out by using analytical expressions, therefore increasing the accuracy of the algebraic system obtained for each one of the studied schemes. The developed numerical programs were applied initially to elastic fracture mechanics and then extended to analyze cohesive cracks. Several numerical examples were solved to verify the accuracy of each one of the studied models, comparing the results with the analytical solutions avaliable in the literature.

Orientador: Leandro Palermo Junior / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Civil, Arquitetura e Urbanismo / Made available in DSpace on 2018-08-11T02:34:56Z (GMT). No. of bitstreams: 1 Figueiredo_LuizGustavode_M.pdf: 920848 bytes, checksum: 436f0a3bed33057f927837f04e2e8804 (MD5) Previous issue date: 2008 / Resumo: A avaliação da influêcia de um modelo coesivo de fratura no comportamento estrutural e a simulação de propagação de fraturas pré-existentes, com a Mecâica da Fratura Elástica Linear (MFEL), em problemas bidimensionais, usando o Método dos Elementos de Contorno Dual (DBEM), é o principal objetivo deste estudo. Problemas elásticos lineares em meio contínuo podem ser resolvidos com a equação integral de contorno de deslocamentos. O Método dos Elementos de Contorno Dual pode ser utilizado para resolver os problemas de fratura, onde a equação integral de contorno de forças de superfície é implementada em conjunto com a equação integral de contorno de deslocamentos. Elementos contínuos, descontínuos e mistos podem ser usados no contorno. Diferentes estrat?ias de posicionamento dos pontos de colocação são discutidas neste trabalho, onde os fatores de intensidade de tensão são avaliados com ténica de extrapolação de deslocamentos em fraturas existentes dos tipos: borda, inclinada e em forma de 'v¿. Um modelo coesivo é utilizado para avaliação de comportamento estrutural de um corpo de prova com fratura de borda segundo diferentes estratégias desenvolvidas: uma análise coesiva geral e uma análise coesiva iterativa, as quais são comparadas com o comportamento não coesivo. A força normal coesiva relaciona-se com o valor da abertura de fratura na direção normal na lei constitutiva na Zona de Processos Coesivos (ZPC). A simulação de propagação de uma fratura de borda existente e sua implementa?o num?ica no DBEM, sob deslocamento imposto, é realizada utilizando o critério da mínima tensão circunferencial. Palavras-chave: Método dos Elementos de Contorno; Métodos dos Elementos de Contorno Dual; Mecânica da Fratura Elástica Linear; Modelos Coesivos; Propagação de Fraturas / Abstract: An evaluation of the effect of the cohesive fracture model on the structural behavior and the crack propagation in pre-existing cracks with the Linear Elastic Fracture Mechanics (LEFM), for two dimensional problems, using the Dual Boundary Element Method (DBEM), is the main purpose of the present study. Linear elastic problems in continuum media can be solved with the boundary integral equation for displacements. The Dual Boundary Element Method can be used to solve fracture problems, where the traction boundary integral equation is employed beyond the displacement boundary integral equation. Conformal and non-conformal interpolations can be employed on the boundary. Different strategies for positioning the collocation points are discussed in this work, where the stress intensity factors are evaluated with the displacement extrapolation method to an existing single edge crack, central slant crack and central kinked crack. A cohesive model is used to evaluate the structural behavior of the specimen with a single edge crack under different strategies: a general cohesive analysis and an iterative cohesive analysis; which are compared with the non-cohesive behavior. The normal cohesive force is dependent of the crack opening value in the normal direction in the constitutive law of the Cohesive Process Zone (CPZ). A crack propagation of an existing single edge crack and its numerical implementation in DBEM, under constrained displacement, is analyzed using the maximum hoop stress criterion. Key Words: Boundary Element Method; Dual Boundary Element Method; Linear Elastic Fracture Mechanic; Cohesive Models; Propagation of Cracks / Mestrado / Estruturas / Mestre em Engenharia Civil

In this study, we consider electrostatics contributed from the molecules in the ionic solution. It plays a significant role in determining the binding affinity of molecules and drugs. We develop the overall framework of computing electrostatic properties for three-dimensional molecular structures, including potential, energy, and forces. These properties are derived from Poisson-Boltzmann equation, a partial differential equation that describes the electrostatic behavior of molecules in ionic solutions. In order to compute these properties, we derived new boundary integral equations and designed a boundary element algorithm based on the linear time fast multipole method for solving the linearized Poisson-Boltzmann equation. Meanwhile, a higher-order parametric formulation called algebraic spline model is used for accurate approximation of the unknown solution of the linearized Poisson-Boltzmann equation. Based on algebraic spline model, we represent the normal derivative of electrostatic potential by surrounding electrostatic potential. This representation guarantees the consistent relation between electrostatic potential and its normal derivative. In addition, accurate numerical solution and fast computation for electrostatic energy and forces are also discussed. In addition, we described our hierarchical modeling and parameter optimization of molecular structures. Based on this technique, we can control the scalability of molecular models for electrostatic computation. The numerical test and experimental results show that the proposed techniques offer an efficient and accurate solution for solving the electrostatic problem of molecules. / text

The boundary element method (BEM) has become a powerful method for the numerical solution of boundary-value problems (BVPs), due to its ability (at least for problems with constant coefficients) of reducing a BVP for a linear partial differential equation (PDE) defined in a domain to an integral equation defined on the boundary, leading to a simplified discretisation process with boundary elements only. On the other hand, the coefficients in the mathematical model of a physical problem typically correspond to the material parameters of the problem. In many physical problems, the governing equation is likely to involve variable coefficients. The application of the BEM to these equations is hampered by the difficulty of finding a fundamental solution. The first part of this thesis will focus on the derivation of the boundary integral equation (BIE) for the Laplace equation, and numerical results are presented for some examples using constant elements. Then, the formulations of the boundary-domain integral or integro-differential equation (BDIE or BDIDE) for heat conduction problems with variable coefficients are presented using a parametrix (Levi function), which is usually available. The second part of this thesis deals with the extension of the BDIE and BDIDE formulations to the treatment of the two-dimensional Helmholtz equation with variable coefficients. Four possible cases are investigated, first of all when both material parameters and wave number are constant, in which case the zero-order Bessel function of the second kind is used as fundamental solution. Moreover, when the material parameters are variable (with constant or variable wave number), a parametrix is adopted to reduce the Helmholtz equation to a BDIE or a BDIDE. Finally, when material parameters are constant (with variable wave number), the standard fundamental solution for the Laplace equation is used in the formulation. In the third part, the radial integration method (RIM) is introduced and discussed in detail. Modifications are introduced to the RIM, particularly the fact that the radial integral is calculated by using a pure boundary-only integral which relaxes the “star-shaped” requirement of the RIM. Then, the RIM is used to convert the domain integrals appearing in both BDIE and BDIDE for heat conduction and Helmholtz equations to equivalent boundary integrals. For domain integrals consisting of known functions the transformation is straightforward, while for domain integrals that include unknown variables the transformation is accomplished with the use of augmented radial basis functions (RBFs). The most attractive feature of the method is that the transformations are very simple and have similar forms for both 2D and 3D problems. Finally, the application of the RIM is discussed for the diffusion equation, in which the parabolic PDE is initially reformulated as a BDIE or a BDIDE and the RIM is used to convert the resulting domain integrals to equivalent boundary integrals. Three cases have been investigated, for homogenous, non-homogeneous and variable coefficient diffusion problems.