Effect of mesh distortion on the accuracy of high order vorticity-velocity CFD approaches

The numerical solution of the incompressible Navier-Stokes equations offers an alternative to experimental analysis of fluid-structure interaction (FSI). We would save a lot of time and effort and help cut back on costs, if we are able to accurately model systems by these numerical solutions. These advantages are even more obvious when considering huge structures like bridges, high rise buildings or even wind turbine blades with diameters as large as 200 meters. The modeling of such processes, however, involves complex multiphysics problems along with complex geometries. This thesis focuses on a novel vorticity-velocity formulation called the Kinematic Laplacian Equation (KLE) to solve the incompressible Navier-stokes equations for such FSI problems. This scheme allows for the implementation of robust adaptive ordinary differential equations (ODE) time integration schemes, allowing us to tackle each problem as a separate module. The current algortihm for the KLE uses an unstructured quadrilateral mesh, formed by dividing each triangle of an unstructured triangular mesh into three quadrilaterals for spatial discretization. This research deals with determining a suitable measure of mesh quality based on the physics of the problems being tackled. This is followed by exploring methods to improve the quality of quadrilateral elements obtained from the triangles and thereby improving the overall mesh quality. A series of numerical experiments were designed and conducted for this purpose and the results obtained were tested on different geometries with varying degrees of mesh density.

Evaluating northern hardwood management using retrospective analysis and diameter distributions

Northern hardwood management was assessed throughout the state of Michigan using data collected on recently harvested stands in 2010 and 2011. Methods of forensic estimation of diameter at breast height were compared and an ideal, localized equation form was selected for use in reconstructing pre-harvest stand structures. Comparisons showed differences in predictive ability among available equation forms which led to substantial financial differences when used to estimate the value of removed timber. Management on all stands was then compared among state, private, and corporate landowners. Comparisons of harvest intensities against a liberal interpretation of a well-established management guideline showed that approximately one third of harvests were conducted in a manner which may imply that the guideline was followed. One third showed higher levels of removals than recommended, and one third of harvests were less intensive than recommended. Multiple management guidelines and postulated objectives were then synthesized into a novel system of harvest taxonomy, against which all harvests were compared. This further comparison showed approximately the same proportions of harvests, while distinguishing sanitation cuts and the future productive potential of harvests cut more intensely than suggested by guidelines. Stand structures are commonly represented using diameter distributions. Parametric and nonparametric techniques for describing diameter distributions were employed on pre-harvest and post-harvest data. A common polynomial regression procedure was found to be highly sensitive to the method of histogram construction which provides the data points for the regression. The discriminative ability of kernel density estimation was substantially different from that of the polynomial regression technique.

Multi-antenna non-line-of-sight identification techniques for target localization in mobile ad-hoc networks

Target localization has a wide range of military and civilian applications in wireless mobile networks. Examples include battle-field surveillance, emergency 911 (E911), traffc alert, habitat monitoring, resource allocation, routing, and disaster mitigation. Basic localization techniques include time-of-arrival (TOA), direction-of-arrival (DOA) and received-signal strength (RSS) estimation. Techniques that are proposed based on TOA and DOA are very sensitive to the availability of Line-of-sight (LOS) which is the direct path between the transmitter and the receiver. If LOS is not available, TOA and DOA estimation errors create a large localization error. In order to reduce NLOS localization error, NLOS identifcation, mitigation, and localization techniques have been proposed. This research investigates NLOS identifcation for multiple antennas radio systems. The techniques proposed in the literature mainly use one antenna element to enable NLOS identifcation. When a single antenna is utilized, limited features of the wireless channel can be exploited to identify NLOS situations. However, in DOA-based wireless localization systems, multiple antenna elements are available. In addition, multiple antenna technology has been adopted in many widely used wireless systems such as wireless LAN 802.11n and WiMAX 802.16e which are good candidates for localization based services. In this work, the potential of spatial channel information for high performance NLOS identifcation is investigated. Considering narrowband multiple antenna wireless systems, two xvNLOS identifcation techniques are proposed. Here, the implementation of spatial correlation of channel coeffcients across antenna elements as a metric for NLOS identifcation is proposed. In order to obtain the spatial correlation, a new multi-input multi-output (MIMO) channel model based on rough surface theory is proposed. This model can be used to compute the spatial correlation between the antenna pair separated by any distance. In addition, a new NLOS identifcation technique that exploits the statistics of phase difference across two antenna elements is proposed. This technique assumes the phases received across two antenna elements are uncorrelated. This assumption is validated based on the well-known circular and elliptic scattering models. Next, it is proved that the channel Rician K-factor is a function of the phase difference variance. Exploiting Rician K-factor, techniques to identify NLOS scenarios are proposed. Considering wideband multiple antenna wireless systems which use MIMO-orthogonal frequency division multiplexing (OFDM) signaling, space-time-frequency channel correlation is exploited to attain NLOS identifcation in time-varying, frequency-selective and spaceselective radio channels. Novel NLOS identi?cation measures based on space, time and frequency channel correlation are proposed and their performances are evaluated. These measures represent a better NLOS identifcation performance compared to those that only use space, time or frequency.

Effect of high order interpolation in the stability and efficiency of the time-integration process in vorticity-velocity CFD algorithms

The numerical solution of the incompressible Navier-Stokes Equations offers an effective alternative to the experimental analysis of Fluid-Structure interaction i.e. dynamical coupling between a fluid and a solid which otherwise is very complex, time consuming and very expensive. To have a method which can accurately model these types of mechanical systems by numerical solutions becomes a great option, since these advantages are even more obvious when considering huge structures like bridges, high rise buildings, or even wind turbine blades with diameters as large as 200 meters. The modeling of such processes, however, involves complex multiphysics problems along with complex geometries. This thesis focuses on a novel vorticity-velocity formulation called the KLE to solve the incompressible Navier-stokes equations for such FSI problems. This scheme allows for the implementation of robust adaptive ODE time integration schemes and thus allows us to tackle the various multiphysics problems as separate modules. The current algorithm for KLE employs a structured or unstructured mesh for spatial discretization and it allows the use of a self-adaptive or fixed time step ODE solver while dealing with unsteady problems. This research deals with the analysis of the effects of the Courant-Friedrichs-Lewy (CFL) condition for KLE when applied to unsteady Stoke’s problem. The objective is to conduct a numerical analysis for stability and, hence, for convergence. Our results confirmthat the time step ∆t is constrained by the CFL-like condition ∆t ≤ const. hα, where h denotes the variable that represents spatial discretization.

Dynamics of settling charged particles in turbulence : theory and experiments

It has been proposed that inertial clustering may lead to an increased collision rate of water droplets in clouds. Atmospheric clouds and electrosprays contain electrically charged particles embedded in turbulent flows, often under the influence of an externally imposed, approximately uniform gravitational or electric force. In this thesis, we present the investigation of charged inertial particles embedded in turbulence. We have developed a theoretical description for the dynamics of such systems of charged, sedimenting particles in turbulence, allowing radial distribution functions to be predicted for both monodisperse and bidisperse particle size distributions. The governing parameters are the particle Stokes number (particle inertial time scale relative to turbulence dissipation time scale), the Coulomb-turbulence parameter (ratio of Coulomb ’terminalar speed to turbulence dissipation velocity scale), and the settling parameter (the ratio of the gravitational terminal speed to turbulence dissipation velocity scale). For the monodispersion particles, The peak in the radial distribution function is well predicted by the balance between the particle terminal velocity under Coulomb repulsion and a time-averaged ’drift’ velocity obtained from the nonuniform sampling of fluid strain and rotation due to finite particle inertia. The theory is compared to measured radial distribution functions for water particles in homogeneous, isotropic air turbulence. The radial distribution functions are obtained from particle positions measured in three dimensions using digital holography. The measurements support the general theoretical expression, consisting of a power law increase in particle clustering due to particle response to dissipative turbulent eddies, modulated by an exponential electrostatic interaction term. Both terms are modified as a result of the gravitational diffusion-like term, and the role of ’gravity’ is explored by imposing a macroscopic uniform electric field to create an enhanced, effective gravity. The relation between the radial distribution functions and inward mean radial relative velocity is established for charged particles.

Bayesian change-point analysis in linear regression model with scale mixtures of normal distributions

In this thesis, we consider Bayesian inference on the detection of variance change-point models with scale mixtures of normal (for short SMN) distributions. This class of distributions is symmetric and thick-tailed and includes as special cases: Gaussian, Student-t, contaminated normal, and slash distributions. The proposed models provide greater flexibility to analyze a lot of practical data, which often show heavy-tail and may not satisfy the normal assumption. As to the Bayesian analysis, we specify some prior distributions for the unknown parameters in the variance change-point models with the SMN distributions. Due to the complexity of the joint posterior distribution, we propose an efficient Gibbs-type with Metropolis- Hastings sampling algorithm for posterior Bayesian inference. Thereafter, following the idea of [1], we consider the problems of the single and multiple change-point detections. The performance of the proposed procedures is illustrated and analyzed by simulation studies. A real application to the closing price data of U.S. stock market has been analyzed for illustrative purposes.

USING AUTO- AND CROSS-CORRELATIONS FROM SEISMIC NOISE TO MONITOR VELOCITY CHANGES AT VILLARRICA VOLCANO, CHILE

We used the Green's functions from auto-correlations and cross-correlations of seismic ambient noise to monitor temporal velocity changes in the subsurface at Villarrica volcano in the Southern Andes of Chile. Campaigns were conducted from March to October 2010 and February to April 2011 with 8 broadband and 6 short-period stations, respectively. We prepared the data by removing the instrument response, normalizing with a root-mean-square method, whitening the spectra, and filtering from 1 to 10 Hz. This frequency band was chosen based on the relatively high background noise level in that range. Hour-long auto- and cross-correlations were computed and the Green's functions stacked by day and total time. To track the temporal velocity changes we stretched a 24 hour moving window of correlation functions from 90% to 110% of the original and cross correlated them with the total stack. All of the stations' auto-correlations detected what is interpreted as an increase in velocity in 2010, with an average increase of 0.13%. Cross-correlations from station V01, near the summit, to the other stations show comparable changes that are also interpreted as increases in velocity. We attribute this change to the closing of cracks in the subsurface due either to seasonal snow loading or regional tectonics. In addition to the common increase in velocity across the stations, there are excursions in velocity on the same order lasting several days. Amplitude decreases as the station's distance from the vent increases suggesting these excursions may be attributed to changes within the volcanic edifice. In at least two occurrences the amplitudes at stations V06 and V07, the stations farthest from the vent, are smaller. Similar short temporal excursions were seen in the auto-correlations from 2011, however, there was little to no increase in the overall velocity.