Herein a fully parallel, upwind and flux-split Finite-Volume Time-Domain (FVTD) numerical engine for solving Maxwell's Equations on unstructured grids is developed. The required background theory for solving Maxwell's Equations using FVTD is given in sufficient detail, including a description of both the temporal and spatial approximations used. The details of the local-time stepping strategy of Fumeaux et al. is included. A global mesh-truncation scheme using field integration over a Huygens' surface is also presented. The capabilities of the FVTD algorithm are augmented with thin-wire and subcell circuit models that permit very flexible and accurate simulations of circuit-driven wire structures. Numerical and experimental validation shows that the proposed models have a wide-range of applications. Specifically, it appears that the thin-wire and subcell circuit models may be very well suited to the simulation of radio-frequency coils used in magnetic resonance imaging systems. A parallelization scheme for the volumetric field solver, combined with the local-time stepping, global mesh-truncation and subcell models is developed that theoretically provides both linear time- and memory scaling in a distributed parallel environment. Finally, the FVTD code is converted to the frequency domain and the possibility of using different flux-reconstruction schemes to improve the iterative convergence of the Finite-Volume Frequency-Domain algorithm is investigated.

The aim of this project is to develop a computational model of the structure and function of the ocular lens, specifically the solute and fluid transport in the lens. The modelling framework was based on finite volume methods. The intracellular and extracellular solute fluxes were modelled using the Nernst-Plank equation with an extra term to capture solute fluxes due to advection. The modelling framework included equations describing the flux through the Na+ /K+ pumps and K+ channels in the surface membrane, and Na+ and Cl- channels in the fibre cell membrane. The intracellular fluid flow between adjacent fibre cells was modelled by a homogenised transmembrane fluid flow equation and the intracellular fluid flow along the fibre cell was modelled as Poiseuille flow. The extracellular fluid flow was modelled as Couette flow with an extra term to capture electro-osmotic flow. The fluid flow through the fibre cell membrane and surface membrane was modelled as transmembrane fluid flow. The governing equations account for the structural properties of the lens, such as the tortuosity of the extracellular cleft, the intracellular and extracellular volume fractions, and the membrane density. A one-dimensional model of the Na+ , K+ , Cl- and fluid transport in the frog lens was developed. This model was based on the analytic model developed by Mathias (1985b). The results were consistent with the results from the analytic model and experimental data. Two versions of the two-dimensional model were developed. In the first model, the parameters were spatially constant except for the distribution of the Na+ /K+ pump currents at the lens surface and the fibre cell angles. The second model was the same, except the extracellular cleft width and fibre cell height was spatially varied to represent the sutures and the diffusion barrier. These models were solved and compared with each other and with experimental data. Compared to the first, the second model predicted a significantly larger circulation of solutes and fluid between the pole and equator. It predicted a 12-20% increase in the penetration of Na+ , K+ and fluid into the lens. The second model also predicted a 300-400% increase in Cl- penetration and, unlike the first model, a Cl- circulation between the poles and equator. This is significant since Cl- is not an actively transported solute. These results highlight the strong structure-function relationship in the lens and the importance of an accurate spatial representation of model parameters. The direction of the current, solute fluxes and fluid flow that were predicted by the model were consistent with experimental data but the magnitude of the surface current was a tenth to a third of the values measure by the vibrating probe. To demonstrate the application of the lens model, the two-dimensional model was used to simulate age-related changes in lens physiology. This was done by increasing the radius of the lens to simulate growth with age. The model predicted an increase in the intracellular Na+ concentration, Cl- concentration and potential, and a decrease in the intracellular K+ concentration with age. These trends were consistent with those observed by Duncan et al. (1989), except for the intracellular K+ concentration, where they reported no change with age. The two-dimensional model forms a foundation for future developments and applications.

The aim of this project is to develop a computational model of the structure and function of the ocular lens, specifically the solute and fluid transport in the lens. The modelling framework was based on finite volume methods. The intracellular and extracellular solute fluxes were modelled using the Nernst-Plank equation with an extra term to capture solute fluxes due to advection. The modelling framework included equations describing the flux through the Na+ /K+ pumps and K+ channels in the surface membrane, and Na+ and Cl- channels in the fibre cell membrane. The intracellular fluid flow between adjacent fibre cells was modelled by a homogenised transmembrane fluid flow equation and the intracellular fluid flow along the fibre cell was modelled as Poiseuille flow. The extracellular fluid flow was modelled as Couette flow with an extra term to capture electro-osmotic flow. The fluid flow through the fibre cell membrane and surface membrane was modelled as transmembrane fluid flow. The governing equations account for the structural properties of the lens, such as the tortuosity of the extracellular cleft, the intracellular and extracellular volume fractions, and the membrane density. A one-dimensional model of the Na+ , K+ , Cl- and fluid transport in the frog lens was developed. This model was based on the analytic model developed by Mathias (1985b). The results were consistent with the results from the analytic model and experimental data. Two versions of the two-dimensional model were developed. In the first model, the parameters were spatially constant except for the distribution of the Na+ /K+ pump currents at the lens surface and the fibre cell angles. The second model was the same, except the extracellular cleft width and fibre cell height was spatially varied to represent the sutures and the diffusion barrier. These models were solved and compared with each other and with experimental data. Compared to the first, the second model predicted a significantly larger circulation of solutes and fluid between the pole and equator. It predicted a 12-20% increase in the penetration of Na+ , K+ and fluid into the lens. The second model also predicted a 300-400% increase in Cl- penetration and, unlike the first model, a Cl- circulation between the poles and equator. This is significant since Cl- is not an actively transported solute. These results highlight the strong structure-function relationship in the lens and the importance of an accurate spatial representation of model parameters. The direction of the current, solute fluxes and fluid flow that were predicted by the model were consistent with experimental data but the magnitude of the surface current was a tenth to a third of the values measure by the vibrating probe. To demonstrate the application of the lens model, the two-dimensional model was used to simulate age-related changes in lens physiology. This was done by increasing the radius of the lens to simulate growth with age. The model predicted an increase in the intracellular Na+ concentration, Cl- concentration and potential, and a decrease in the intracellular K+ concentration with age. These trends were consistent with those observed by Duncan et al. (1989), except for the intracellular K+ concentration, where they reported no change with age. The two-dimensional model forms a foundation for future developments and applications.

The aim of this project is to develop a computational model of the structure and function of the ocular lens, specifically the solute and fluid transport in the lens. The modelling framework was based on finite volume methods. The intracellular and extracellular solute fluxes were modelled using the Nernst-Plank equation with an extra term to capture solute fluxes due to advection. The modelling framework included equations describing the flux through the Na+ /K+ pumps and K+ channels in the surface membrane, and Na+ and Cl- channels in the fibre cell membrane. The intracellular fluid flow between adjacent fibre cells was modelled by a homogenised transmembrane fluid flow equation and the intracellular fluid flow along the fibre cell was modelled as Poiseuille flow. The extracellular fluid flow was modelled as Couette flow with an extra term to capture electro-osmotic flow. The fluid flow through the fibre cell membrane and surface membrane was modelled as transmembrane fluid flow. The governing equations account for the structural properties of the lens, such as the tortuosity of the extracellular cleft, the intracellular and extracellular volume fractions, and the membrane density. A one-dimensional model of the Na+ , K+ , Cl- and fluid transport in the frog lens was developed. This model was based on the analytic model developed by Mathias (1985b). The results were consistent with the results from the analytic model and experimental data. Two versions of the two-dimensional model were developed. In the first model, the parameters were spatially constant except for the distribution of the Na+ /K+ pump currents at the lens surface and the fibre cell angles. The second model was the same, except the extracellular cleft width and fibre cell height was spatially varied to represent the sutures and the diffusion barrier. These models were solved and compared with each other and with experimental data. Compared to the first, the second model predicted a significantly larger circulation of solutes and fluid between the pole and equator. It predicted a 12-20% increase in the penetration of Na+ , K+ and fluid into the lens. The second model also predicted a 300-400% increase in Cl- penetration and, unlike the first model, a Cl- circulation between the poles and equator. This is significant since Cl- is not an actively transported solute. These results highlight the strong structure-function relationship in the lens and the importance of an accurate spatial representation of model parameters. The direction of the current, solute fluxes and fluid flow that were predicted by the model were consistent with experimental data but the magnitude of the surface current was a tenth to a third of the values measure by the vibrating probe. To demonstrate the application of the lens model, the two-dimensional model was used to simulate age-related changes in lens physiology. This was done by increasing the radius of the lens to simulate growth with age. The model predicted an increase in the intracellular Na+ concentration, Cl- concentration and potential, and a decrease in the intracellular K+ concentration with age. These trends were consistent with those observed by Duncan et al. (1989), except for the intracellular K+ concentration, where they reported no change with age. The two-dimensional model forms a foundation for future developments and applications.

The aim of this project is to develop a computational model of the structure and function of the ocular lens, specifically the solute and fluid transport in the lens. The modelling framework was based on finite volume methods. The intracellular and extracellular solute fluxes were modelled using the Nernst-Plank equation with an extra term to capture solute fluxes due to advection. The modelling framework included equations describing the flux through the Na+ /K+ pumps and K+ channels in the surface membrane, and Na+ and Cl- channels in the fibre cell membrane. The intracellular fluid flow between adjacent fibre cells was modelled by a homogenised transmembrane fluid flow equation and the intracellular fluid flow along the fibre cell was modelled as Poiseuille flow. The extracellular fluid flow was modelled as Couette flow with an extra term to capture electro-osmotic flow. The fluid flow through the fibre cell membrane and surface membrane was modelled as transmembrane fluid flow. The governing equations account for the structural properties of the lens, such as the tortuosity of the extracellular cleft, the intracellular and extracellular volume fractions, and the membrane density. A one-dimensional model of the Na+ , K+ , Cl- and fluid transport in the frog lens was developed. This model was based on the analytic model developed by Mathias (1985b). The results were consistent with the results from the analytic model and experimental data. Two versions of the two-dimensional model were developed. In the first model, the parameters were spatially constant except for the distribution of the Na+ /K+ pump currents at the lens surface and the fibre cell angles. The second model was the same, except the extracellular cleft width and fibre cell height was spatially varied to represent the sutures and the diffusion barrier. These models were solved and compared with each other and with experimental data. Compared to the first, the second model predicted a significantly larger circulation of solutes and fluid between the pole and equator. It predicted a 12-20% increase in the penetration of Na+ , K+ and fluid into the lens. The second model also predicted a 300-400% increase in Cl- penetration and, unlike the first model, a Cl- circulation between the poles and equator. This is significant since Cl- is not an actively transported solute. These results highlight the strong structure-function relationship in the lens and the importance of an accurate spatial representation of model parameters. The direction of the current, solute fluxes and fluid flow that were predicted by the model were consistent with experimental data but the magnitude of the surface current was a tenth to a third of the values measure by the vibrating probe. To demonstrate the application of the lens model, the two-dimensional model was used to simulate age-related changes in lens physiology. This was done by increasing the radius of the lens to simulate growth with age. The model predicted an increase in the intracellular Na+ concentration, Cl- concentration and potential, and a decrease in the intracellular K+ concentration with age. These trends were consistent with those observed by Duncan et al. (1989), except for the intracellular K+ concentration, where they reported no change with age. The two-dimensional model forms a foundation for future developments and applications.

Thesis (Ph. D.)--University of Texas at Austin, 2006. / Vita. Includes bibliographical references.

Thesis (Ph. D.)--University of Washington, 2005. / Vita. Includes bibliographical references (p. 214-234).

Currently standard first order single-point upstream weighting methods are employed in reservoir simulation for integrating the essentially hyperbolic system components. These methods introduce both coordinate-line numerical diffusion (even in 1-D) and cross-wind diffusion into the solution that is grid and geometry dependent. These effects are particularly important when steep fronts and shocks are present and for cases where flow is across grid coordinate lines. In this thesis, families of novel edge-based and cell-based truly multidimensional upwind formulations that upwind in the direction of the wave paths in order to minimise crosswind diffusion are presented for hyperbolic conservation laws on structured and unstructured triangular and quadrilateral grids in two dimensions. Higher resolution as well as higher order multidimensional formulations are also developed for general structured and unstructured grids. The schemes are coupled with existing consistent and efficient continuous CVD (MPFA) Darcy flux approximations. They are formulated using an IMPES (Implicit in Pressure Explicit in Saturation) strategy for solving the coupled elliptic (pressure) and hyperbolic (saturation) system of equations governing the multi-phase multi-component flow in porous media. The new methods are compared with single point upstream weighting for two-phase and three-component two-phase flow problems. The tests arc conducted on both structured and unstructured grids and involve full-tensor coefficient velocity fields in homogeneous and heterogeneous domains. The comparisons demonstrate the benefits of multidimensional and higher order multidimensional schemes in terms of improved front resolution together with significant reduction in cross-wind diffusion.

CoordenaÃÃo de AperfeiÃoamento de Pessoal de NÃvel Superior / à corrente o uso de inspeÃÃo nÃo-destrutiva ultrassÃnica na detecÃÃo de descontinuidades nos mais diversos materiais utilizados na indÃstria Adicionalmente informaÃÃes sobre a microestrutura do material inspecionado podem ser obtidas a partir do processamento da sÃrie temporal produzida durante a inspeÃÃo A simulaÃÃo do ensaio ultrassÃnico representa uma importante ferramenta para o entendimento e previsÃo da interaÃÃo da onda mecÃnica com o meio No entanto faz-se necessÃrio primeiramente modelar o meio que reproduza as caracterÃsticas de uma amostra objeto de estudo por onde a onda propaga Cinco meios unidimensionais compostos por domÃnios (representando grÃos) com tamanho mÃdio distinto e a mesma densidade mÃdia foram definidos neste trabalho SimulaÃÃes de propagaÃÃo de ondas ultrassÃnicas nos meios modelados foram executadas para quatro diferentes frequÃncias de ondas Concomitantemente foram capturados sinais ultrassÃnicos sobre cinco amostras de aÃo contendo diferentes tamanhos mÃdios de grÃo utilizando transdutores de 2.25 5.0 10.0 e 20.0 MHz Todos os sinais obtidos foram submetidos à detrended fluctuation analysis DFA e rescaled range analysis R/S duas tÃcnicas de anÃlise de flutuaÃÃes em sÃries temporais com vista a filtrar informaÃÃes espÃrias e avaliar influÃncia das variÃveis selecionadas (tamanho de grÃo e frequÃncia do sinal) sobre os sinais ultrassÃnicos obtidos Por fim à feita uma comparaÃÃo entre os dados simulados e experimentais e avaliaÃÃo da qualidade da simulaÃÃo / It is usual the application of ultrasonic non-destructive evaluation to detect discontinuities in different materials applied in industry Furthermore information about the microstructure of the inspected material can be obtained by signal processing of time series produced during the inspection Simulation of ultrasonic testing can be an important tool to help the understanding and predicting the interaction of mechanical wave in materials First of all computational materials modeling to reproduce the characteristics of specimens through which the wave propagates is necessary Five different one-dimensional materials composed of domains (grains) with different average size and same density were designed in this work Simulations of ultrasonic wave propagation in the modeled materials were performed at four different wave frequencies Concomitantly ultrasonic signals were acquired from five steel samples containing different average grain sizes using probes with central frequency of 225 5 10 and 20 MHz Detrended fluctuation analysis DFA and rescaled range analysis R/S two techniques for analyzing fluctuations in time series were used to process the signals in order to filter out spurious information and evaluate the influence of selected variables (grain size and frequency of the signal) on the ultrasonic signals obtained Finally simulated and experimental data and compared in order to evaluate the simulation performance

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