Made available in DSpace on 2014-06-11T19:23:38Z (GMT). No. of bitstreams: 0 Previous issue date: 2010-08-30Bitstream added on 2014-06-13T20:30:31Z : No. of bitstreams: 1 rodrigues_tt_me_ilha.pdf: 2332044 bytes, checksum: 6e277868f01ea21a46dfbf5c827109a7 (MD5) / Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) / Fundação de Ensino Pesquisa e Extensão de Ilha Solteira (FEPISA) / A compreensão do escoamento em válvulas de compressores herméticos alternativos é de fundamental importância para introduzir modificações no projeto delas de maneira a aumentar a performance dos compressores, e por fim, dos ciclos de refrigeração. A válvula do compressor é um dispositivo ímpar, umas vez que seu funcionamento se dá pela ação da pressão exercida pelo escoamento, caracterizando um problema de forte interação fluido- estrutura. O uso da modelagem numérica através das ferramentas da mecânica dos fluidos computacional (CFD) tem se destacado como a alternativa mais dinâmica para o estudo do fenômeno. O trabalho desenvolvido foi voltado para o estudo numérico do escoamento através do difusor radial, o qual é um modelo simplificado da válvula, com o emprego do Método da Fronteira Imersa com Modelo Físico Virtual para a modelagem do disco superior do difusor (palheta). O ponto forte desta metodologia é que a representação de regiões sólidas é feita pelo cálculo de um campo de força, o qual é introduzido nas equações das células na vizinhança do sólido. Este procedimento dispensa o uso de malhas que se adaptam ao corpo, possibilitando o uso de malhas cartesianas convencionas para modelar geometrias complexas e móveis. A metodologia foi acoplada com a solução das equações governantes do escoamento em coordenadas cilíndricas através do Método dos Volumes Finitos. Inicialmente, a metodologia foi validada, utilizando como dados de referência resultados provenientes de estudos numéricos e experimentais, e foi avaliada a influência dos parâmetros do procedimento na qualidade final dos resultados. Na segunda etapa foram desenvolvidos estudos preliminares referentes ao movimento do disco superior, com a imposição artificial dos processos de abertura e fechamento da válvula. Os resultados obtidos mostraram que a metodologia adotada... / The fully understanding of the flow through automatic valves of alternative hermetic compressors is essentiall to introduce modifications in its project aiming the improvement of the compressor performance and, also, the refrigeration cycle. The compressor valve is a singular device, once its operation is ruled by the flow pressure, characterizing a case with a strong fluid-structure interaction. The using of numerical tools trough the methods of computational fluid dynamics (CFD) has gained especial attention due to its flexibility to study the phenomenon. The present work was developed to study numerically the flow through the radial diffuser, which is a simplified model of the valve, with the employment of the Immersed Boundary Method with Virtual Physical Model to modeling the superior disk (valve reed). The main advantage of this methodology is that the modeling of solid boundaries is performed with the calculus of a force field, which is introduced in the cells equations nearby the solid. This procedure dispenses the using of body-fitted meshes, enabling the adoption of conventional Cartesian meshes to model complex and moving geometries. The methodology was coupled with the solution of the governing equations in cylindrical coordinates though the Finite Volume Method. Firstly, the methodology was validated, confronting the results obtained with data from numerical and experimental studies, where the influence of the main parameters in the quality of the final results was evaluated. In the second step were developed preliminary studies concerning the movement of the superior disk, whose opening and closing movements were artificially imposed. The results obtained showed that the adopted methodology is quit promising and flexible, and can be employed in more refined studies to the comprehension of the flow through the valve regarding the fluid-structure interaction that rules the problem

Made available in DSpace on 2014-06-11T19:23:39Z (GMT). No. of bitstreams: 0 Previous issue date: 2009-09-08Bitstream added on 2014-06-13T19:09:39Z : No. of bitstreams: 1 lacerda_jf_me_ilha.pdf: 4631781 bytes, checksum: cad33ad7c5cac9de6cec08fd94b419e7 (MD5) / Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) / Nesse trabalho resolve-se numericamente o escoamento em difusores radiais, os quais têm sido utilizados como modelo para o estudo do escoamento em válvulas automáticas de compressores de refrigeração. As equações governantes do escoamento, escritas no sistema de coordenadas cilíndricas, são resolvidas utilizando um código numérico baseado no Método dos Volumes Finitos. O Método da Fronteira Imersa, em conjunto com o Modelo Físico Virtual, foi implementado no código numérico e utilizado para representar a região sólida imersa no escoamento. Inicialmente, o código numérico foi utilizado para resolver o problema do escoamento em torno de um cilindro de base quadrada, como parte do processo de validação do código. O confronto dos resultados numéricos com dados da literatura indicou a validação parcial do código. Posteriormente, realizou-se um estudo preliminar do comportamento da solução do escoamento no difusor radial em relação a diversos parâmetros geométricos e de simulação numérica, com o objetivo de identificar a configuração numérica capaz de fornecer, simultaneamente, resultados satisfatórios com o menor custo computacional. Usando esta configuração, o código numérico foi validado através da comparação dos resultados da distribuição de pressão sobre o disco frontal (palheta) do difusor com dados experimentais da literatura, para duas distâncias entre disco frontal e disco inferior (assento), s=0,02 e 0,025 cm, e números de Reynolds variando entre 1500 e 2500. As comparações entre esses resultados mostraram que a metodologia utilizada é adequada para estudar o problema. Finalmente, a geometria do disco inferior foi modificada através da inserção de um chanfro com três ângulos de inclinação (30, 45 e 60º), com o objetivo de avaliar sua influência sobre o comportamento da distribuição de pressão sobre o disco frontal... / In this work the flow in radial diffusers, which have been used as a model to study the flow in refrigeration compressors valves, is solved numerically. The governing equations, written in cylindrical coordinates, are solved using a numerical code based on the Finite Volume Method. The Immersed Boundary Method, with the Virtual Physical Method, was implemented in the numerical code and used to represent the solid region immersed in the flow. Initially, the numerical code was used to solve the flow around a square base cylinder, as part of the code validation. The comparison of the numerical results with literature data indicated the partial validation of the code. Afterwards it was performed a preliminary study of the behavior of the flow solution in the radial diffuser relating to several geometrical and numerical parameters, with the objective of identifying a configuration capable of providing, simultaneously, satisfactory results with the smaller computational cost. Using this configuration, the numerical code was validated through the comparison with experimental pressure distribution on the frontal disk (reed) for two gaps between the frontal disk and inferior disk (seat), s=0.020 and 0.025 cm, and Reynolds numbers varying between 1500 and 2500. These comparisons have shown that the implemented methodology is suitable to study this problem. Finally, the inferior disk geometry was modified by inserting a chamfer with three inclination angles (30, 45 e 60º), with the objective of evaluating its influence on the pressure distribution on the frontal disk. The decreasing of the total pressure gradient through the flow for increasing inclination angles indicates less amount of energy to drive the flow. This is an important result that can be used to design refrigeration compressors with lower compression power

Orientador: José Luiz Gasche / Banca: Sérgio Said Mansur / Banca: Aristeu da Silveira Neto / Resumo: Nesse trabalho resolve-se numericamente o escoamento em difusores radiais, os quais têm sido utilizados como modelo para o estudo do escoamento em válvulas automáticas de compressores de refrigeração. As equações governantes do escoamento, escritas no sistema de coordenadas cilíndricas, são resolvidas utilizando um código numérico baseado no Método dos Volumes Finitos. O Método da Fronteira Imersa, em conjunto com o Modelo Físico Virtual, foi implementado no código numérico e utilizado para representar a região sólida imersa no escoamento. Inicialmente, o código numérico foi utilizado para resolver o problema do escoamento em torno de um cilindro de base quadrada, como parte do processo de validação do código. O confronto dos resultados numéricos com dados da literatura indicou a validação parcial do código. Posteriormente, realizou-se um estudo preliminar do comportamento da solução do escoamento no difusor radial em relação a diversos parâmetros geométricos e de simulação numérica, com o objetivo de identificar a configuração numérica capaz de fornecer, simultaneamente, resultados satisfatórios com o menor custo computacional. Usando esta configuração, o código numérico foi validado através da comparação dos resultados da distribuição de pressão sobre o disco frontal (palheta) do difusor com dados experimentais da literatura, para duas distâncias entre disco frontal e disco inferior (assento), s=0,02 e 0,025 cm, e números de Reynolds variando entre 1500 e 2500. As comparações entre esses resultados mostraram que a metodologia utilizada é adequada para estudar o problema. Finalmente, a geometria do disco inferior foi modificada através da inserção de um chanfro com três ângulos de inclinação (30, 45 e 60º), com o objetivo de avaliar sua influência sobre o comportamento da distribuição de pressão sobre o disco frontal... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: In this work the flow in radial diffusers, which have been used as a model to study the flow in refrigeration compressors valves, is solved numerically. The governing equations, written in cylindrical coordinates, are solved using a numerical code based on the Finite Volume Method. The Immersed Boundary Method, with the Virtual Physical Method, was implemented in the numerical code and used to represent the solid region immersed in the flow. Initially, the numerical code was used to solve the flow around a square base cylinder, as part of the code validation. The comparison of the numerical results with literature data indicated the partial validation of the code. Afterwards it was performed a preliminary study of the behavior of the flow solution in the radial diffuser relating to several geometrical and numerical parameters, with the objective of identifying a configuration capable of providing, simultaneously, satisfactory results with the smaller computational cost. Using this configuration, the numerical code was validated through the comparison with experimental pressure distribution on the frontal disk (reed) for two gaps between the frontal disk and inferior disk (seat), s=0.020 and 0.025 cm, and Reynolds numbers varying between 1500 and 2500. These comparisons have shown that the implemented methodology is suitable to study this problem. Finally, the inferior disk geometry was modified by inserting a chamfer with three inclination angles (30, 45 e 60º), with the objective of evaluating its influence on the pressure distribution on the frontal disk. The decreasing of the total pressure gradient through the flow for increasing inclination angles indicates less amount of energy to drive the flow. This is an important result that can be used to design refrigeration compressors with lower compression power / Mestre

O estudo do comportamento de um perfil de uma seção aerolástica típica, com Reynolds na faixa de microaeronaves, constitui o principal foco deste trabalho, tomando como objetivo a estimativa de parâmetros do fenômeno de flutter. A pesquisa analisa o escoamento de um fluido sobre um corpo (cilindro e perfil de aerofólio) em estado estacionário e oscilante, em escoamento de velocidade constante, e, especificamente, o fenômeno de flutter. As equações de Navier-Stokes, com termo de força, são resolvidas pelo método da fronteira virtual para modelagem da interface escoamento/estrutura, representada pela geometria de um corpo de geometria complexa. Na discretização das equações governantes foi utilizado o método de diferenças finitas, sobre malhas deslocadas, com avanço temporal das velocidades do escoamento por meio de um esquema de Runge-Kutta de ordem 4. Os códigos computacionais, para as simulações das diretrizes e a lógica de cálculo, foram criados no contexto deste trabalho. A verificação foi feita através do método da solução manufaturada por meio de um problema fictício, que tem uma solução analítica conhecida, e que preenche as condições de contorno implementadas no código. O modelo da fronteira virtual é testado para os casos de escoamento sobre cilindro de base quadrada, cilindro de base circular e perfil de aerofólio tipo NACA0012, com malhas regular e não regular, e para condições estacionária e sob oscilação forçada. Foi estudado o comportamento de formação de vórtices, provocados por escoamento uniforme sobre o perfil de aerofólio, através dos coeficientes de arrasto, sustentação e pressão com visualização por meio da vorticidade e linhas de corrente, para vários ângulos de ataque e oscilação forçada com elevação e rotação em torno de um pivô posicionado no centro geométrico do perfil (50% da corda). Finalmente, é apresentada uma determinação numérica das características aeroelásticas para o perfil de aerofólio NACA0012, em escoamento de número de Reynolds ultra baixo (Re = 1.000), e parâmetros de flutter para um caso de baixa frequência de oscilação. / The behavior study of a profile of a typical aerolastic section, with Reynolds in range of micro aerial vehicle, is the main focus of this work, taking as objective the estimation of parameters of flutter phenomenon. The research analyzes of the flow of a incompressible fluid on a body (cylinder and airfoil profile) at steady state and oscillating with constant speed and, specifically, the flutter phenomenon. The Navier-Stokes equations, with force term, are solved by virtual boundary method for modeling interface flow/structure, represented by the geometry of a body of complex geometry. In discretization of the governing equations, the method of finite differences on staggered grid, with temporal advancement of discharge velocity through a Runge-Kutta of order 4. The computer codes, for simulations guidelines and logic calculation, were created in the context of this work. The verification was done by method ofmanufactured solution through a fictional problem, which has a known analytical solution, and satisfies the boundary conditions implemented in code. The model of the virtual boundary is tested for cases of flow over a square cylinder, circular cylinder and profile of a NACA0012 airfoil type, with regular and non-regular meshes, over stationary and forced oscillation conditions. We studied the behavior of vortex formation, caused by uniform flow over the airfoil profile, by the drag, lift and pressure coefficients with view through the vorticity and streamlines for various attack angles and forced oscillation with plunge and pich around a pivot witch was positioned at the geometric airfoil profile (half chord). Finally, it is presented a numerical determination of aeroelastic characteristics for the NACA0012 airfoil profile, flow under ultra low Reynolds number, and flutter parameters for a case of low oscillation frequency.

O escoamento em torno de corpos tem sido objeto de estudo de muitos pesquisadores e é muito explorado experimental e computacionalmente, devido a sua grande aplicabilidade na engenharia. No entanto, simular computacionalmente este tipo de escoamento requer uma atenção especial ao escolher o tipo malha a ser utilizado. Em muitos casos faz-se necessário o uso de uma malha que se adapte ao contorno do obstáculo, o que pode ocasionar um aumento no esforço computacional. Um maneira de contornar este problema é a utilização do Método das Fronteiras Imersas, que possibilita o uso de malha cartesiana na simulação computacional do escoamento em torno de obstáculos. Isso é possível através da adição de um termo forçante nas equações que modelam o escoamento, e assim as forças que agem sobre o contorno do corpo são transferidas diretamente para a malha. O objetivo deste trabalho de mestrado foi implementar o método das Fronteiras Imersas e simular o escoamento em torno de um cilindro circular em repouso, movimentando-se na mesma direção do escoamento, na direção perpendicular ao escoamento, ou rotacionando em torno do próprio eixo. As simulações computacionais possibilitaram a captura do fenômeno de Atrelagem Síncrona, caracterizado pela sincronia entre a frequência de desprendimento natural de vórtices e a frequência de oscilação do mesmo. O Método das Fronteiras Imersas mostrou um ótimo desempenho quando comparado a resultados experimentais e numéricos encontrados na literatura / The flow around bodies have been studied by many researchers. Both experimental and computational approaches have been extensively explored in researches on flow around bodies and have been applied in many engeneering problems. However, to choose an appropriate type of mesh to perform computational simulations of this type of problem requires special attention. In many cases, it is necessary to use a mesh that is able to conform to the boundary if a given obstacle. The need to perform this adaptation may increase the computational effort. The Immersed Boundary Method enables the use of cartesian meshes to perform computational simulations of flows around obstacles. The idea of this method is to add a forcing term in the equations that model the flow. Thus, the forces applied on the body boundaries are directly transfered to the mesh. The aim of this work was to perform a computational implementation of the Immersed Boundary Method to simulate the flow over a oscilating circular cylinder. This oscilation may be inline with the flow, cross-flow, or rotating. The computational simulations enabled the capture of the lock-in phenomena, which consists of the syncronization between the vortex shedding frequency and the cylinder oscilation frequency. The results obtained from the computational simulations using the Immersed Boundary Method were in good agreement with the numerical and experimental results found in the literature

Dans cette thèse, une nouvelle méthode de frontières immergées a été développée pour la simulation d'interaction fluide-structure, appelée la méthode de frontières immergées mobiles (en langage anglo-saxon: MIBM). L'objectif principal de cette nouvelle méthode est de déplacer arbitrairement les solides à géométrie complexe dans un fluide visqueux incompressible, sans remailler le domaine fluide. Cette nouvelle méthode a l'avantage d'imposer la condition de non-glissement à l'interface d'une manière exacte via une force sans introduire des constantes artificielles modélisant la structure rigide. Cet avantage conduit également à la satisfaction de la condition CFL avec un pas de temps plus grand. Pour un calcul précis de la force induite par les frontières mobiles, un système linéaire a été introduit et résolu par la méthode de gradient conjugué. La méthode proposée peut être intégrée facilement dans des solveurs résolvant les équations de Navier-Stokes. Dans ce travail la MIBM a été mise en œuvre en couplage avec un solveur fluide utilisant une méthode de projection adaptée pour obtenir des solutions d'ordre deux en temps et en espace. Le champ de pression a été obtenu par l'équation de Poisson qui a été résolue à l'aide de la méthode du gradient conjugué préconditionné par la méthode multi-grille. La combinaison de ces deux méthodes a permis un gain de temps considérable par rapport aux méthodes classiques de la résolution des systèmes linéaires. De plus le code de calcul développé a été parallélisé sur l'unité graphique GPU équipée de la bibliothèque CUDA pour aboutir à des hautes performances de calcul. Enfin, comme application de nos travaux sur la MIBM, nous avons étudié le couplage "fort" d'interaction fluide-structure (IFS). Pour ce type de couplage, un schéma implicite partitionné a été adopté dans lequel les conditions à l'interface sont satisfaites via un schéma de type "point fixe". Pour réduire le temps de calcul inhérent à cette application, un nouveau schéma de couplage a été proposé pour éviter la résolution de l'équation de Poisson durant les itérations du "point fixe". Cette nouvelle façon de résoudre les problèmes IFS a montré des performances prometteuses pour des systèmes en IFS complexe. / In this thesis a novel non-body conforming mesh formulation is developed, called the moving immersed boundary method (MIBM), for the numerical simulation of fluid-structure interaction (FSI). The primary goal is to enable solids of complex shape to move arbitrarily in an incompressible viscous fluid, without fitting the solid boundary motion with dynamic meshes. This novel method enforces the no-slip boundary condition exactly at the fluid-solid interface with a boundary force, without introducing any artificial constants to the rigid body formulation. As a result, large time step can be used in current method. To determine the boundary force more efficiently in case of moving boundaries, an additional moving force equation is derived and the resulting system is solved by the conjugate gradient method. The proposed method is highly portable and can be integrated into any fluid solver as a plug-in. In the present thesis, the MIBM is implemented in the fluid solver based on the projection method. In order to obtain results of high accuracy, the rotational incremental pressure correction projection method is adopted, which is free of numerical boundary layer and is second order accurate. To accelerate the calculation of the pressure Poisson equation, the multi-grid method is employed as a preconditioner together with the conjugate gradient method as a solver. The code is further parallelized on the graphics processing unit (GPU) with the CUDA library to enjoy high performance computing. At last, the proposed MIBM is applied to the study of two-way FSI problem. For stability and modularity reasons, a partitioned implicit scheme is selected for this strongly coupled problem. The interface matching of fluid and solid variables is realized through a fixed point iteration. To reduce the computational cost, a novel efficient coupling scheme is proposed by removing the time-consuming pressure Poisson equation from this fixed point interaction. The proposed method has shown a promising performance in modeling complex FSI system.

Underwater explosions (UNDEX) and a ship's vulnerability to them are problems of interest in early-stage ship design. A series of events occur sequentially in an UNDEX scenario in both the fluid and structural domains and these events happen over a wide range of time and spatial scales. Because of the complexity of the physics involved, it is a common practice to separate the description of UNDEX into early-time and late-time, and far-field and near-field. The research described in this dissertation is focused on the simulation of near-field and early-time UNDEX. It assembles a hybrid framework of algorithms to provide results while maintaining computational efficiency. These algorithms include Runge-Kutta, Discontinuous Galerkin, Level Set, Direct Ghost Fluid and Embedded Boundary methods. Computational fluid dynamics (CFD) solvers are developed using this framework of algorithms to demonstrate the computational methods and their ability to effectively and efficiently solve UNDEX problems. Contributions, made in the process of satisfying the objective of this research include: the derivation of eigenvectors of flux Jacobians and their application to the implementation of the slope limiter in the fluid discretization; the three-dimensional extension of Direct Ghost Fluid Method and its application to the multi-fluid treatment in UNDEX flows; the enforcement of an improved non-reflecting boundary condition and its application to UNDEX simulations; and an improvement to the projection-based embedded boundary method and its application to fluid-structure interaction simulations of UNDEX problems. / Doctor of Philosophy / Underwater explosions (UNDEX) and a ship's vulnerability to them are problems of interest in early-stage ship design. A series of events occur sequentially in an UNDEX scenario in both the fluid and structural domains and these events happen over a wide range of time and spatial scales. Because of the complexity of the physics involved, it is a common practice to separate the description of UNDEX into early-time and late-time, and far-field and near-field. The research described in this dissertation is focused on the simulation of near-field and early-time UNDEX. It assembles a hybrid framework of algorithms to provide results while maintaining computational efficiency. These algorithms include Runge-Kutta, Discontinuous Galerkin, Level Set, Direct Ghost Fluid and Embedded Boundary methods. Computational fluid dynamics (CFD) solvers are developed using this framework of algorithms to demonstrate these computational methods and their ability to effectively and efficiently solve UNDEX problems.

[pt] O escoamento de cápsulas suspensas em uma fase líquida através de canais e capilares micrométricos representa um problema complexo que ocorre em diferentes aplicações, de glóbulos vermelhos em hemodinâmica até escoamento em meios porosos. Em aplicações de meios porosos, a compreensão da dinâmica na microescala é fundamental para avaliar o comportamento macroscópico do escoamento. Canais e capilares com constrição podem ser usados para modelar uma garganta conectando dois poros adjacentes. O escoamento de uma cápsula suspensa através de tais modelos foi analisado para avaliar as características do escoamento considerando os efeitos inerciais (isto é, número de Reynolds finito), incluindo a máxima diferença de pressão necessária para empurrar uma cápsula através da constrição em função do raio da cápsula, a tensão inicial e o material da membrana, geometria do canal e do capilar, assim como as condições de escoamento. De fato, neste estudo, a resposta da pressão é fundamental para avaliar o efeito de bloqueio da cápsula. As fases líquidas internas e externas foram descritas pelas equações de Navier-Stokes, enquanto que a dinâmica da membrana da cápsula foi modelada por uma estrutura flexível 1-D tipo mola. O problema de interação fluido-estrutura foi resolvido usando o método de elementos finitos acoplado ao método de fronteira imersa. Os resultados mostraram a redução da mobilidade da fase contínua devido à presença da cápsula através da constrição. Tais resultados podem ser usados para projetar microcápsulas para bloquear caminhos preferenciais de fluxo da água no processo de deslocamento de óleo em meios porosos. / [en] The flow of capsules suspended in a liquid phase through small channels and capillaries poses a complex problem presented in different applications, from red blood cells on hemodynamics to flow in porous media. In applications of porous media, the understanding of microscale dynamics is fundamental to assess the macroscopic flow behavior. Constricted channels and capillaries can be used to model a pore throat connecting two adjacent pore bodies. The flow of a suspended capsule through such models was analyzed to evaluate the flow characteristics considering inertial effects (i.e. finite Reynolds numbers), including the maximum pressure difference required to push a capsule through the constriction as a function of capsule radius, initial membrane tension, membrane material, channel and capillary geometries, as well as flow conditions. In fact, in this study, the pressure response is fundamental in order to assess the capsule blocking mechanism. Inner and outer liquid phases were described by the Navier-Stokes equations and capsule membrane dynamics was modeled by a 1-D spring-like flexible structure. The fluid-structure interaction problem was solved using the finite element method coupled with the immersed boundary method. Results showed the mobility reduction of the continuous phase due to the presence of a capsule as it flows through the constriction. Such results can be used to design microcapsules to block preferential water flow paths in oil displacement process in porous media.

In this dissertation, we consider the Hull-White term structure problem with the boundary value condition given as the payoff of a European bond option. We restrict ourselves to the case where the parameters of the Hull-White model are strictly positive constants and from the risk neutral valuation formula, we first derive simple closed–form expression for pricing European bond option in the Hull-White extended Vasicek model framework. As the European option can be exercised only on the maturity date, we then examine the case of early exercise opportunity commonly called American option. With the analytic representation of American bond option being very hard to handle, we are forced to resort to numerical experiments. To do it excellently, we transform the Hull-White term structure equation into the diffusion equation and we first solve it through implicit, explicit and Crank-Nicolson (CN) difference methods. As these standard finite difference methods (FDMs) require truncation of the domain from infinite to finite one, which may deteriorate the computational efficiency for American bond option, we try to build a CN method over an unbounded domain. We introduce an exact artificial boundary condition in the pricing boundary value problem to reduce the original to an initial boundary problem. Then, the CN method is used to solve the reduced problem. We compare our performance with standard FDMs and the results through illustration show that our method is more efficient and accurate than standard FDMs when we price American bond option. / Mathematical Sciences / (M.Sc. (Mathematics))

In this dissertation, we consider the Hull-White term structure problem with the boundary value condition given as the payoff of a European bond option. We restrict ourselves to the case where the parameters of the Hull-White model are strictly positive constants and from the risk neutral valuation formula, we first derive simple closed–form expression for pricing European bond option in the Hull-White extended Vasicek model framework. As the European option can be exercised only on the maturity date, we then examine the case of early exercise opportunity commonly called American option. With the analytic representation of American bond option being very hard to handle, we are forced to resort to numerical experiments. To do it excellently, we transform the Hull-White term structure equation into the diffusion equation and we first solve it through implicit, explicit and Crank-Nicolson (CN) difference methods. As these standard finite difference methods (FDMs) require truncation of the domain from infinite to finite one, which may deteriorate the computational efficiency for American bond option, we try to build a CN method over an unbounded domain. We introduce an exact artificial boundary condition in the pricing boundary value problem to reduce the original to an initial boundary problem. Then, the CN method is used to solve the reduced problem. We compare our performance with standard FDMs and the results through illustration show that our method is more efficient and accurate than standard FDMs when we price American bond option. / Mathematical Sciences / (M.Sc. (Mathematics))