Thesis (Ph. D.)--University of Washington, 2006. / Vita. Includes bibliographical references (leaves 149-159).

This thesis is concerned with the modeling of the stator of a piezoelectric traveling wave rotary ultrasonic motor. Existing models for piezoelectric traveling wave rotary ultrasonic motors are either too complicated to be used in motor control or do not reflect the real behavior of the motor and are of limited use in developing a controller for the motor. Finite Element methods have been used in the past to examine the properties of piezoelectric structures however, the Finite Volume Method has always been ruled out without justification. The main goal of this thesis is to provide a Finite Volume modeling approach for the stator of the piezoelectric traveling wave rotary ultrasonic motor taking into account the basic theoretical principles from piezoelectricity and structural mechanics. This model can in future be extended to develop a complete model of the motor in addition to other piezoelectric structures. The Finite Volume Method is shown to have the following specific advantages over the Finite Element Method especially for structures with simple geometries: 1. the Finite Volume Method respects the PDEs conservation law structure due to the fact that the fluxes are conserved between cells/domains/subregions, 2. the Finite Volume Method involves only surface integrals thus making it easier to implement a rotor-stator contact model as the contact mechanism occurs at the boundary of the stator, and 3. the Finite Volume Method yields a system of ODEs that more intuitively map onto circuit simulation software. The Finite Volume Method is initially used to model a simple piezoelectric plate. A corresponding circuit of the piezoelectric plate model, based on the Finite Volume Method, is generated. Two additional but more complex models are considered: one for a unimorph plate and one for the stator of an ultrasonic motor. The modeling results obtained with the Finite Volume Method are validated by comparing them with the results obtained with Finite Element simulations performed with COMSOL. Two test platforms designed to test and validate the Finite Volume and COMSOL results for the simple piezoelectric plates and piezoelectric traveling wave rotary ultrasonic motors are also presented in this thesis.

This thesis is concerned with the modeling of the stator of a piezoelectric traveling wave rotary ultrasonic motor. Existing models for piezoelectric traveling wave rotary ultrasonic motors are either too complicated to be used in motor control or do not reflect the real behavior of the motor and are of limited use in developing a controller for the motor. Finite Element methods have been used in the past to examine the properties of piezoelectric structures however, the Finite Volume Method has always been ruled out without justification. The main goal of this thesis is to provide a Finite Volume modeling approach for the stator of the piezoelectric traveling wave rotary ultrasonic motor taking into account the basic theoretical principles from piezoelectricity and structural mechanics. This model can in future be extended to develop a complete model of the motor in addition to other piezoelectric structures. The Finite Volume Method is shown to have the following specific advantages over the Finite Element Method especially for structures with simple geometries: 1. the Finite Volume Method respects the PDEs conservation law structure due to the fact that the fluxes are conserved between cells/domains/subregions, 2. the Finite Volume Method involves only surface integrals thus making it easier to implement a rotor-stator contact model as the contact mechanism occurs at the boundary of the stator, and 3. the Finite Volume Method yields a system of ODEs that more intuitively map onto circuit simulation software. The Finite Volume Method is initially used to model a simple piezoelectric plate. A corresponding circuit of the piezoelectric plate model, based on the Finite Volume Method, is generated. Two additional but more complex models are considered: one for a unimorph plate and one for the stator of an ultrasonic motor. The modeling results obtained with the Finite Volume Method are validated by comparing them with the results obtained with Finite Element simulations performed with COMSOL. Two test platforms designed to test and validate the Finite Volume and COMSOL results for the simple piezoelectric plates and piezoelectric traveling wave rotary ultrasonic motors are also presented in this thesis.

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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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.