Thesis (Ph. D.)--University of Washington, 2002. / Vita. Includes bibliographical references (p. 178-185).

Radio-frequency microelectromechanical systems (RF MEMS) are widely used for contact actuators and capacitive switches. These devices typically consist of a metallic membrane which is activated by a time-periodic electrostatic force and makes periodic contact with a contact pad. The increase in switch capacitance at contact causes the RF signal to be deflected and the switch thus closes. Membrane motion is damped by the surrounding gas, typically air or nitrogen. As the switch opens and closes, the flow transitions between the continuum and rarefied regimes. Furthermore, creep is a critical physical mechanism responsible for the failure in these devices, especially those operating at high RF power. Simultaneous and accurate modeling of all these different physics is required to understand the dynamical membrane response in these devices and to estimate device lifetime and to improve MEMS reliability. It is advantageous to model fluid and structural mechanics and electrostatics within a single comprehensive numerical framework to facilitate coupling between them. In this work, we develop a single unified finite volume method based numerical framework to study this multi-physics problem in RF MEMS. Our objective required us to develop structural solvers, fluid flow solvers, and electrostatic solvers using the finite volume method, and efficient mechanisms to couple these different solvers. A particular focus is the development of flow solvers which work efficiently across continuum and rarefied regimes. A number of novel contributions have been made in this process. Structural solvers based on a fully implicit finite volume method have been developed for the first time. Furthermore, strongly implicit fluid flow solvers have also been developed that are valid for both continuum and rarefied flow regimes and which show an order of magnitude speed-up over conventional algorithms on serial platforms. On parallel platforms, the solution techniques developed in this thesis are shown to be significantly more scalable than existing algorithms. The numerical methods developed are used to compute the static and dynamic response of MEMS. Our results indicate that our numerical framework can become a computationally efficient tool to model the dynamics of RF MEMS switches under electrostatic actuation and gas damping. / text

The development of a Magneto-hydrodynamics (MHD) numerical tool to study high density thermal plasmas in plasma acceleration devices is presented. The MHD governing equations represent eight conservation equations for the evolution of density, momentum, energy and induced magnetic fields in a plasma. A matrix-free implicit method is developed to solve these conservation equations within the framework of an unstructured grid finite volume formulation. The analytic form of the convective flux Jacobian is derived for general unstructured grids. A Lower Upper Symmetric Gauss Seidel (LU-SGS) technique is developed as part of the implicit scheme. A coloring based algorithm for parallelization of this technique is also presented and its computational efficiency is compared with a global matrix solve technique that uses the GMRES (Generalized Minimum Residual) algorithm available in the PETSc (Portable Extensible Toolkit for Scientific computation) libraries. The verification cases used for this study are the MHD shock tube problem in one, two and three dimensions, the oblique shock and the Hartmann flow problem. It is seen that the matrix free method is comparatively faster and shows excellent scaling on multiple cores compared to the global matrix solve technique. The numerical model was thus verified against the above mentioned standard test cases and two application problems were studied. These include the simulation of plasma deflagration phenomenon in a coaxial plasma accelerator and a novel high speed flow control device called the Rail Plasma Actuator (RailPAc). Experimental studies on coaxial plasma accelerators have revealed two different modes of operation based on the delay between gas loading and discharge ignition. Longer delays lead to the detonation or the snowplow mode while shorter delays lead to the relatively efficient stationary or deflagration mode. One of the theories that explain the two different modes is based on plasma resistivity. A numerical modeling study is presented here in the context of a coaxial plasma accelerator and the effect of plasma resistivity is dealt with in detail. The simulated results pertaining to axial distribution of radial currents are compared with experimental measurements which show good agreement with each other. The simulations show that magnetic field diffusion is dominant at lower conductivities which tend to form a stationary region of high current density close to the inlet end of the device. Higher conductivities led to the formation of propagating current sheet like features due to greater convection of magnetic field. This study also validates the theory behind the two modes of operation based on plasma resistivity. The RailPAc (Rail Plasma Actuator) is a novel flow control device that uses the magnetic Lorentz forces for fluid flow actuation at atmospheric pressures. Experimental studies reveal actuation ~ 10-100 m/s can be achieved with this device which is much larger than conventional electro-hydrodynamic (EHD) force based plasma actuators. A magneto-hydrodynamics simulation study of this device is presented. The model is further developed to incorporate applied electric and magnetic fields seen in this device. The snowplow model which is typically used for studying pulsed plasma thrusters is used to predict the arc velocities which agrees well with experimental measurements. Two dimensional simulations were performed to study the effect of Lorentz forcing and heating effects on fluid flow actuation. Actuation on the order of 100 m/s is attained at the head of the current sheet due to the effect of Lorentz forcing alone. The inclusion of heating effects led to isotropic blast wave like actuation which is detrimental to the performance of RailPAc. This study also revealed the deficiencies of a single fluid model and a more accurate multi-fluid approach is proposed for future work. / text

The problem of real-time simulation of ocean surface waves, ship movement and the coupling in between is tackled, and a number of different methods are covered and discussed. Among these methods, the finite volume method has been implemented in an attempt to solve the problem, along with the compressible Euler equations, an octree based staggered grid which allows for easy adaptive mesh refinement, the volume of fluid method and a variant of the Hyper-C advection scheme for compressible flows for advection of the phase fraction field. The process of implementing the methods that were chosen proved to be tricky in many ways, as they involve a large number of advanced topics, and the implementation that was implemented in this thesis work suffered from numerous issues. There were for example problems with keeping the interface intact, as well as a harsh restriction on the time step size due to the CFL condition. Improvements required to make the method sustainable for real-time applications are discussed, and a few suggestions on alternative approaches that are already in use for similar purposes are also given and discussed. Furthermore, a method for compensating for gain/loss of mass when solving the incompressible flow equations with an inaccurately solved pressure Poisson equation is presented and discussed. A momentum conservative method for transporting the velocity field on staggered grids without introducing unnecessary smearing is also presented and implemented. A simple, physically based illumination model for sea surfaces is derived, discussed and compared to the Blinn–Phong shading model, although it is never implemented. Finally, a two-dimensional partial differential equation in the spatial domain for simulating water surface waves for mildly varying bottom topography is derived and discussed, although it is deemed to be too slow for real-time purposes and is therefore never implemented. / <p>This publication differs from the printed version of the report in the sense that links are blue in this version and black in the printed version.</p>

A two dimensional hydrodynamic model describing the solar wind interaction with the local interstellar medium, which surrounds the solar system, is used to study the heliosphere both as a steady-state- and dynamic structure. The finite volume method used to solve the associated system of hydrodynamic equations numerically is discussed in detail. Subsequently the steady state heliosphere is studied for both the case where the solar wind and the interstellar medium are assumed to consist of protons only, as well as the case where the neutral hydrogen population in the interstellar medium is taken into account. It is shown that the heliosphere forms as three waves, propagating away from the initial point of contact between the solar wind and interstellar matter, become stationary. Two of these waves become stationary at sonic points, forming the termination shock and bow shock respectively. The third wave becomes stationary as a contact discontinuity, called the heliopause. It is shown that the position and geometry of the termination shock, heliopause and bow shock as well as the plasma flow characteristics of the heliosphere largely depend on the dynamic pressure of either the solar wind or interstellar matter. The heliosphere is modelled as a dynamic structure, including both the effects of the solar cycle and short term variations in the solar wind observed by a range of spacecraft over the past ~ 30 years. The dynamic model allows the calculation of an accurate record of the heliosphere state over the past ~ 30 years. This record is used to predict the time at which the Voyager 2 spacecraft will cross the termination shock. Voyager 1 observations of 10 MeV cosmic ray electrons are then used in conjunction with a cosmic ray modulation model to constrain the record of the heliosphere further. It is shown that the dynamic hydrodynamic model describes the heliosphere accurately within a margin of error of ±0.7 years and ±3 AU. The model predicts that Voyager 2 crossed the termination shock in 2007, corresponding to preliminary results from observations indicating that the crossing occurred in August 2007. / Thesis (M.Sc. (Physics))--North-West University, Potchefstroom Campus, 2008.

The most commonly used method for the time-domain Maxwell equations is the Finite-Difference Time-Domain method (FDTD). This is an explicit, second-order accurate method, which is used on a staggered Cartesian grid. The main drawback with the FDTD method is its inability to accurately model curved objects and small geometrical features. This is due to the Cartesian grid, which leads to a staircase approximation of the geometry and small details are not resolved at all. This thesis presents different ways to circumvent this drawback, but still take advantage of the benefits of the FDTD method. An approach to avoid staircasing errors but still retain the efficiency of the FDTD method is to use a hybrid grid. A few layers of unstructured cells are used close to curved objects and a Cartesian grid is used for the rest of the domain. For the choice of solver on the unstructured grid two different alternatives are compared: an explicit Finite-Volume Time-Domain (FVTD) solver and an implicit Finite-Element Time-Domain (FETD) solver. The hybrid solvers calculate the scattering from complex objects much more efficiently compared to using FDTD on highly resolved Cartesian grids. For the same accuracy in the solution roughly a factor of 10 in memory requirements and a factor of 20 in execution time are gained. The ability to model features that are small relative to the cell size is often important in electromagnetic simulations. In this thesis a technique to generalize a well-known subcell model for thin wires, in order to take arbitrarily oriented wires in FETD and FDTD into account, is proposed. The method gives considerable modeling flexibility compared to earlier methods and is proven stable. The results show excellent consistency and very good accuracy on different antenna configurations. The recursive convolution method is often used to model frequency dispersive materials in FDTD. This method is used to enable modeling of such materials in the unstructured FVTD and FETD solvers. The stability of both solvers is analyzed and their accuracy is demonstrated by computing the radar cross section for homogeneous as well as layered spheres with frequency dependent permittivity.

A two dimensional hydrodynamic model describing the solar wind interaction with the local interstellar medium, which surrounds the solar system, is used to study the heliosphere both as a steady-state- and dynamic structure. The finite volume method used to solve the associated system of hydrodynamic equations numerically is discussed in detail. Subsequently the steady state heliosphere is studied for both the case where the solar wind and the interstellar medium are assumed to consist of protons only, as well as the case where the neutral hydrogen population in the interstellar medium is taken into account. It is shown that the heliosphere forms as three waves, propagating away from the initial point of contact between the solar wind and interstellar matter, become stationary. Two of these waves become stationary at sonic points, forming the termination shock and bow shock respectively. The third wave becomes stationary as a contact discontinuity, called the heliopause. It is shown that the position and geometry of the termination shock, heliopause and bow shock as well as the plasma flow characteristics of the heliosphere largely depend on the dynamic pressure of either the solar wind or interstellar matter. The heliosphere is modelled as a dynamic structure, including both the effects of the solar cycle and short term variations in the solar wind observed by a range of spacecraft over the past ~ 30 years. The dynamic model allows the calculation of an accurate record of the heliosphere state over the past ~ 30 years. This record is used to predict the time at which the Voyager 2 spacecraft will cross the termination shock. Voyager 1 observations of 10 MeV cosmic ray electrons are then used in conjunction with a cosmic ray modulation model to constrain the record of the heliosphere further. It is shown that the dynamic hydrodynamic model describes the heliosphere accurately within a margin of error of ±0.7 years and ±3 AU. The model predicts that Voyager 2 crossed the termination shock in 2007, corresponding to preliminary results from observations indicating that the crossing occurred in August 2007. / Thesis (M.Sc. (Physics))--North-West University, Potchefstroom Campus, 2008.

The present research focuses on the development and computer implementation of a novel threedimensional, anisotropic turbulence model not only capable of handling complex geometries but also the turbulence driven secondary currents. The model equations comprise advanced algebraic Reynolds stress models in conjunction with Reynolds Averaged Navier-Stokes equations. In order to tackle the complex geometry of compound meandering channels, the body-fitted orthogonal coordinate system is used. The finite volume method with collocated arrangement of variables is used for discretization of the governing equations. Pressurevelocity coupling is achieved by the standard iterative SIMPLE algorithm. A central differencing scheme and upwind differencing scheme are implemented for approximation of diffusive and convective fluxes on the control volume faces respectively. A set of algebraic equations, derived after discretization, are solved with help of Stones implicit matrix solver. The model is validated against standard benchmarks on simple and compound straight channels. For the case of compound meandering channels with varying sinuosity and floodplain height, the model results are compared with the published experimental data. It is found that the present method is able to predict the mean velocity distribution, pressure and secondary flow circulations with reasonably good accuracy. In terms of engineering applications, the model is also tested to understand the importance of turbulence driven secondary currents in slightly curved channel. The development of this unique model has opened many avenues of future research such as flood risk management, the effects of trees near the bank on the flow mechanisms and prediction of pollutant transport.

Dielectric Barrier Discharge (DBD) excimer lamp is a very attractive source for Ultraviolet (UV) radiation. It has a number of advantages compared to the mercury lamp which is the main lamp used in the industry for UV production. Some of these advantages are instant UV radiation (no warm-up period), narrow UV spectrum, longer life times and simple construction. The DBD UV lamp can be used in number of applications like water disinfection, Plasma Display Panels (PDP) and surface treatment in the semiconductor industry. Yet, the full industrial application of this lamp still faces some problems mainly related to finding the optimum electrical driver to maximize the efficiency of such a lamp. This includes the type of the electrical waveform to generate and the power electronic driver to produce it. In this thesis, firstly a physically based circuit model for the DBD lamp using the Finite Volume Method (FVM) is developed. This model provides the electrical and optical characteristics of the lamp. Using this model the sensitivity of the lamp efficiency to the proposed electrical waveform has been determined. Secondly, the order of this FVM model has been reduced to obtain a model which is used in the design procedure of the proposed driver. Since the DBD lamp has a capacitive nature, a current controlled driver is proposed in this thesis as opposed to most of the published drivers which are voltage controlled drivers. The design of this driver is intended to enhance the electrical to optical efficiency of the lamp and therefore enhancing the overall efficiency of the system. The driver topology permits direct control of the peak lamp current and the operating frequency of the supplied current to the DBD lamp. The width of the current pulses is determined by the transformer magnetizing inductance and the lamp capacitance. Experimental results of the proposed driver connected to a XeCl DBD lamp are presented to validate the performance of the driver and to prove the concept of such a current controlled driver. The proposed driver performance is compared to a voltage source driver which was also implemented. The proposed driver produced higher overall system efficiency but at the expense of a reduction in the driver efficiency as compared to the voltage source driver. The complete system, which consists of the developed FVM based model and the equivalent circuit of the proposed driver, was simulated and the results were compared to the experimental results to validate the accuracy of the developed model for the DBD lamp.

A Cartesian method for solution of the steady two-dimensional Euler equations is produced. Dynamic data structures are used and both geometric and solution-based adaptations are applied. Solution adaptation is achieved through solution-based gradient information. The finite volume method is used with cell-centered approach. The solution is converged to a steady state by means of an approximate Riemann solver. Local time step is used for convergence acceleration. A multistage time stepping scheme is used to advance the solution in time. A number of internal and external flow problems are solved in order to demonstrate the efficiency and accuracy of the method.