Efficiency is one of the key issues in numerical simulation of large-scale problems with complex 3-D geometry. Traditional domain based methods, such as finite element methods, may not be suitable for these problems due to, for example, the complexity of mesh generation. The Boundary Element Method (BEM), based on boundary integral formulations (BIE), offers one possible solution to this issue by discretizing only the surface of the domain. However, to date, successful applications of the BEM are mostly limited to linear and continuum problems. The challenges in the extension of the BEM to nonlinear problems or problems with non-continuum boundary conditions (BC) include, but are not limited to, the lack of appropriate BIE and the difficulties in the treatment of the volume integrals that result from the nonlinear terms. In this thesis work, new approaches and techniques based on the BEM have been developed for 3-D nonlinear problems and Stokes problems with slip BC. For nonlinear problems, a major difficulty in applying the BEM is the treatment of the volume integrals in the BIE. An efficient approach, based on the precorrected-FFT technique, is developed to evaluate the volume integrals. In this approach, the 3-D uniform grid constructed initially to accelerate surface integration is used as the baseline mesh to evaluate volume integrals. The cubes enclosing part of the boundary are partitioned using surface panels. No volume discretization of the interior cubes is necessary. This grid is also used to accelerate volume integration. Based on this approach, accelerated BEM solvers for non-homogeneous and nonlinear problems are developed and tested. Good agreement is achieved between simulation results and analytical results. Qualitative comparison is made with current approaches. Stokes problems with slip BC are of particular importance in micro gas flows such as those encountered in MEMS devices. An efficient approach based on the BEM combined with the precorrected-FFT technique has been proposed and various techniques have been developed to solve these problems. As the applications of the developed method, drag forces on oscillating objects immersed in an unbounded slip flow are calculated and validated with either analytic solutions or experimental results.

Since the micro-electro mechanical system microphone, MEMS microphone, has the advantages of superior sound quality, low power consumption, higher temperature resistance and anti-noise ability in used. The researchers therefore have studied the functions of MEMS microphone since 1980s. The MEMS microphones is applied as the part of 3G mobile phone in the market. Though the functions of microphone are improved by manufacturing process technique and new material designed, this study tends to provide a new, low-cost and rapid design idea to gain the performance in chamber of microphone. Taguchi method and BEASY software, which is boundary element method, are combined to evaluate the results of the design in sound field. Taguchi method is a famous method in industrial design to find out relations between system parameters and chamber size. BEASY is a tool for sound field analysis in the research. The result from Taguchi method appears the sound pressure level gain about 2.2 dB to 2.4 dB due to the change of microphone chamber size only. It is also interested in studying the optimization design for position of microphone. It is displayed that the location of port is closer to the boundary of chip will also increase about 0.3 dB to 0.6dB sound pressure level in sound field. The higher frequency of sound source will also create larger sound pressure level at two corners on the port.

This work studied the productivity evaluation and well test analysis of horizontal wells. The major components of this work consist of a 3D coupled reservoir/wellbore model, a productivity evaluation, a deconvolution technique, and a nonlinear regression technique improving horizontal well test interpretation. A 3D coupled reservoir/wellbore model was developed using the boundary element method for realistic description of the performance behavior of horizontal wells. The model is able to flexibly handle multiple types of inner and outer boundary conditions, and can accurately simulate transient tests and long-term production of horizontal wells. Thus, it can serve as a powerful tool in productivity evaluation and analysis of well tests for horizontal wells. Uncertainty of productivity prediction was preliminarily explored. It was demonstrated that the productivity estimates can be distributed in a broad range because of the uncertainties of reservoir/well parameters. A new deconvolution method based on a fast-Fourier-transform algorithm is presented. This new technique can denoise "noisy" pressure and rate data, and can deconvolve pressure drawdown and buildup test data distorted by wellbore storage. For cases with no rate measurements, a "blind" deconvolution method was developed to restore the pressure response free of wellbore storage distortion, and to detect the afterflow/unloading rate function using Fourier analysis of the observed pressure data. This new deconvolution method can unveil the early time behavior of a reservoir system masked by variable-wellbore-storage distortion, and thus provides a powerful tool to improve pressure transient test interpretation. The applicability of the method is demonstrated with a variety of synthetic and actual field cases for both oil and gas wells. A practical nonlinear regression technique for analysis of horizontal well testing is presented. This technique can provide accurate and reliable estimation of well-reservoir parameters if the downhole flow rate data are available. In the situation without flow rate measurement, reasonably reliable parameter estimation can be achieved by using the detected flow rate from blind deconvolution. It has the advantages of eliminating the need for estimation of the wellbore storage coefficient and providing reasonable estimates of effective wellbore length. This technique provides a practical tool for enhancement of horizontal well test interpretation, and its practical significance is illustrated by synthetic and actual field cases.

Thesis (Ph. D.)--University of Missouri-Columbia, 1999. / Typescript. Vita. Includes bibliographical references (leaves 95-97). Also available on the Internet.

Thesis (Ph. D.)--University of Missouri-Columbia, 1999. / Typescript. Vita. Includes bibliographical references (leaves 95-97). Also available on the Internet.

Thesis (Ph. D.)--Brigham Young University. Dept. of Mathematics, 2004. / Includes bibliographical references (p. 113-117).

Thesis (M.S.)--Mississippi State University. Department of Computational Engineering. / Title from title screen. Includes bibliographical references.

Although many fracture models are based on two-dimensional plane strain approximations, accurately predicting fracture propagation geometry requires accounting for the three-dimensional aspects of fractures. In this study, we implemented 3-D displacement discontinuity (DD) boundary element modeling to investigate the following intrinsically 3-D natural or hydraulic fracture propagation problems: the effect of fracture height on lateral propagation of vertical natural fractures, joint development in the vicinity of normal faults, and hydraulic fracture height growth and non-planar propagation paths. Fracture propagation is controlled by stress intensity factor (SIF) and its determination plays a central role in LEFM. The DD modeling is used to evaluate SIF in Mode I, II and III at the tip of an arbitrarily-shaped embedded crack by using crack-tip element displacement discontinuity. We examine the accuracy of SIF calculation is for rectangular, penny-shaped, and elliptical planar cracks. Using the aforementioned model for lateral propagation of overlapping fractures shows that the curving path of overlapping fractures is strongly influenced by the spacing-to-height ratio of fractures, as well as the differential stress magnitude. We show that the angle of intersection between two non-coincident but parallel en-echelon fractures depends strongly on the fracture height-to-spacing ratio, with intersection angles being asymptotic for "tall" fractures (large height-to-spacing ratios) and nearly orthogonal for "short" fractures. Stress perturbation around normal faults is three-dimensionally heterogeneous. That perturbation can result in joint development at the vicinity of normal faults. We examine the geometrical relationship between genetically related normal faults and joints in various geologic environments by considering a published case study of fault-related joints in the Arches National Park region, Utah. The results show that joint orientation is dependent on vertical position with respect to the normal fault, the spacing-to-height ratio of sub-parallel normal faults, and Poisson's ratio of the media. Our calculations represent a more physically reasonable match to measured field data than previously published, and we also identify a new mechanism to explain the driving stress for opening mode fracture propagation upon burial of quasi-elastic rocks. Hydraulic fractures may not necessarily start perpendicular to the minimum horizontal remote stress. We use the developed fracture propagation model to explain abnormality in the geometry of fracturing from misaligned horizontal wellbores. Results show that the misalignment causes non-planar lateral propagation and restriction in fracture height and fracture width in wellbore part. / text

A panel method derived from inviscid irrotational flow theory and utilizing hyperboloid panels is developed and applied to the simulation of steady fully wetted flows inside water-jet pumps and rocket engine inducers. The source and dipole influence coefficients of the hyperboloid panels are computed using Gauss quadrature. The present method solves the boundary value problem subject to a uniform inflow directly by discretizing the blade, casing/shroud and hub geometries with panels. The Green's integral equation and the influence coefficients for the water-jet/inducer problem are defined and solved by allocating constant strength sources and dipoles on the blade, hub and casing surfaces and constant strength dipoles on the shed wake sheets from the rotor/ stator blades. The rotor- stator interaction is accomplished using an iterative procedure which considers the effects between the rotor and the stator, via circumferentially averaged induced velocities. Finally, the hydrodynamic performance predictions for the water-jet pump and the inducer from the present method are validated against existing experimental data and numerical results from Reynolds Averaged Navier- Stokes (RANS) solvers. / text

The performance of a horizontal axis marine current turbine is predicted by three numerical methods, vortex lattice method MPUF-3A, boundary element method PROPCAV and a commercial RANS solver FLUENT. The predictions are compared with the experimental measurements for the same turbine model. A fully unsteady wake alignment is utilized in order to model the realistic wake geometry of the turbine. A lifting line theory based method is developed to produce the optimum circulation distribution for turbines and propellers and a lifting line theory based database searching method is used to achieve the optimum circulation distribution for tidal turbines. A nonlinear optimization method (CAVOPT-3D) and another database-searching design method (CAVOPT-BASE) are utilized to design the blades of marine current turbines and marine propellers. A design procedure for the tidal turbine is proposed by using the developed methods successively. Finally, an interactive viscous/potential flow method is utilized to analyze the effect of nonuniform inflow on the performance of tidal turbines. / text