This dissertation presents models for turbulent flow and transport by currents and long waves in large domain. From the Navier-Stokes equations, a fully nonlinear depth-integrated equation model for weakly dispersive, turbulent and rotational flow is derived by a perturbation approach based on long wave scaling. The same perturbation approach is applied for the derivation of a depth-integrated transport equation. As the results, coherent structures generated by the turbulence induced by the bottom friction and topography can be predicted very reasonably. The three dimensional turbulence effects are incorporated into the flow model by employing a back scatter model. The back scatter model makes it possible to predict turbulent transport: It contributes to the energy transport and the lateral turbulent diffusion through relying on the turbulent intensity, not by relying on an empirical diffusion constant. The inherent limitation of the depth-integrated transport equation, that is, the limitation for the near field prediction is recognized in the derivation and the numerical simulation. To solve the derived equation set, a highly accurate and stable finite volume scheme numerical solver is developed. Thus, the numerical solver can predict dispersive and nonlinear wave propagation with minimal error. Also, good stability is achieved enough to be applied to the dam-break flows and undular tidal bores. In addition, a robust moving boundary scheme based on simple physical conditions is presented, which can extend the applicability area of the depth-integrated models. By the comparison study with experimental data, it is expected that the numerical model can provide high confidence results for the wave and current transformations including shocks and undular bores on complex bathymetry and topography. For the accurate near field transport prediction, a three dimensional transport model in ?-coordinate coupled with the depth-integrated flow model is developed. Like the other models, this model is also intended for large domain problems, and yet efficient and accurate in the far field and near field together.

In this paper we present a finite volume method for a two-dimensional Black-Scholes equation with stochastic volatility governing European option pricing. In this work, we first formulate the Black-Scholes equation with a tensor (or matrix) diffusion coefficient into a conversative form. We then present a finite volume method for the resulting equation, based on a fitting technique proposed for a one-dimensional Black-Scholes equation. We show that the method is monotone by proving that the system matrix of the discretized equation is an M-matrix. Numerical experiments, performed to demonstrate the usefulness of the method, will be presented.

The effects on heat transfer in a two-dimensional parallel plate channel with sixteen porous baffles in a staggered arrangement with a uniform heat flux heating applied to the top and bottom walls has been numerically investigated. Developing Flow (DF) was considered for this study. The Brinkman-Forchheimer-extended Darcy model was used for modeling the heat transfer and fluid flow through the porous baffles. The flow was assumed to be laminar. A finite volume based method in conjunction with the SIMPLEC algorithm was used to solve the model equations. Calculations were made by varying several independent parameters such as Reynolds number (Re), Darcy number ⎞ (Da), thermal conductivity ratio ⎛⎜ k e kf ⎠⎟ , baffle thickness ( * ) , non-dimensional w ⎝ baffle spacing ( * ) , and non-dimensional baffle height ( * ) . w The results of the study established that porous baffles out perform solid baffles from a pressure drop point of view. However, porous baffles under perform solid baffles from a heat transfer point of view. The ratio representing increase in heat transfer per unit increase in pumping power (heat transfer performance ratio) was found to be less than unity for all cases. Increasing the Darcy number was found to produce less desirable heat transfer enhancement ratios. Increasing the non-dimensional baffle spacing (d/w) and the baffle aspect ratio (H/w) were found to enhance heat transfer.

Thesis (M.S.)--Oregon State University, 2010. / Printout. Includes bibliographical references (leaves 77-78). Also available on the World Wide Web.

Optimal large eddy simulation (OLES) is an approach to LES sub-grid modeling that requires multi-point correlation data as input. Until now, this has been obtained by analyzing DNS statistics. In the finite-volume OLES formulation studied here, under the assumption of small-scale homogeneity and isotropy, these correlations can be theoretically determined from Kolmogorov inertial-range theory, small-scale isotropy, along with the quasi-normal approximation. These models are expressed as generalized quadratic and linear finite volume operators that represent the convective momentum flux. These finite volume operators have been analyzed to determine their characteristics as numerical approximation operators and as models of small-scale effects. In addition, the dependence of the model operators on the anisotropy of the grid and on the size of the stencils is analyzed to develop idealized general operators that can be used on general grids. The finite volume turbulence operators developed here will be applicable in a wide range of LES problems. / text

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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.