By combining the high-order accuracy of spectral expansions with the locality and geometric flexibility of finite elements, spectral elements are an attractive option for the next generation of numerical climate models. Crucial to their construction is the configuration of nodes in an element — casual placement leads to polynomial fits exhibiting Runge phenomena manifested by wild spatial oscillations. I provide highorder triangular elements suitable for incorporation into existing spectral element codes. Constructed from a variety of measures of optimality, these nodes possess the best interpolation error norms discovered to date. Motivated by the need to accurately determine these error norms, I present an optimization method suitable for finding extrema in a triangle. It marries a branch and bound algorithm to a quadtree smoothing scheme. The resulting scheme is both robust and efficient, promising general applicability. In order to qualitatively evaluate these nodal distributions, I introduce the concept of a Lagrangian Voronoi tessellation. This partitioning of the triangle illustrates the regions over which each node dominates. I argue that distant and disconnected regions are undesirable as they exhibit a non-physical influence. Finally, I have discovered a link between point distributions in the simplex and on the hypersphere. Through a simple transformation, a distance metric is defined permitting the construction of Voronoi diagrams and the calculation of mesh norms.

This dissertation presents a methodology to simulate the dispersion of water droplets in the air flow typical of an Icing Tunnel. It is based on the understanding the physical parameters that influence the uniformity and the distribution of cloud of droplets in the airflow and to connect them with analytical parameters which may be used to describe the dispersion process. Specifically it investigates the main geometrical and physical parameters contributing to the droplets dispersion at different tunnel operative conditions, finding a consistent numerical approach to reproduce the local droplets dynamic, quantifying the possible limits of commercial CFD methods, pulling out the empirical parameters/constant needing to simulate properly the local conditions and validating the results with calibrated experiment. An overview of the turbulence and multiphase flow theories, considered relevant to the Icing Tunnel environment, is presented as well as basic concepts and terminology of particle dispersion. Taylor’s theory of particle dispersion has been taken as starting point to explain further historical development of discrete phase dispersion. Common methods incorporated in commercial CFD software are explained and relative shortcomings underlined. The local aerodynamic condition within tunnel, which are required to perform the calculation with the Lagrangian particle equation of motions, are generated numerically using different turbulent models and are compared to the historical K-ε model. Verification of the calculation is performed with grid independency studies. Stochastic Separated Flow methods are applied to compute the particle trajectories. The Discrete Random Walk, as described in the literature, has been used to perform particle dispersion analysis. Numerical settings in the code are related to the characteristics of the local turbulent condition such as turbulence intensity and length scales. Cont/d.

Heterogeneity of surfaces is often included in mathematical treatments of colloid transport and deposition as an afterthought, if at all. Most previous models of colloid transport and deposition have employed idealizations and simplifications such as assuming smooth collector surfaces with uniform chemical properties. This research proposes a new heterogeneous interaction model (HIM) to account for colloidal forces between particles and heterogeneous substrates. Extending the approach employed with the HIM, the inclusion of convection and diffusion in the model leads to a Lagrangian particle tracking model (PTM) for predicting colloid transport and deposition on a planar substrate containing one or more protruding asperities in the presence of shear flow. An important part of the PTM is an accurate rendering of the fluid flow field around the model substrate, which is obtained from a numerical solution of the Stokes equations. A simple approximation of the particle-substrate hydrodynamic interactions was developed for the PTM based on the universal hydrodynamic correction functions. This model was employed to quantitatively predict how presence of asperities on a collector can influence the deposition of particles on the substrate in shear flow. Flow field modifications due to the substrate's physical heterogeneity -- coupled with hydrodynamic interactions -- and the lateral migration (colloidal) forces near chemically heterogeneous substrates yield remarkably diverse deposition probabilities and deposit morphologies. The general approach of this research, which involves the use of the HIM in conjunction with the Brownian PTM, results in the first simulation tool of its kind to attempt to quantify deposition on heterogeneous substrates.

Thesis (Ph. D.)--Ohio University, June, 1998. / Title from PDF t.p.

Thesis (Ph. D.)--University of Western Sydney, 2004. / Includes bibliographical references.

Thesis (Ph. D.)--University of Missouri-Columbia, 1997. / Typescript. Vita. Includes bibliographical references (leaves 119-128). Also available on the Internet.

Thesis (Ph. D.)--Missouri University of Science and Technology, 2009. / Vita. The entire thesis text is included in file. Title from title screen of thesis/dissertation PDF file (viewed August 14, 2009) Includes bibliographical references (p. 68-71).

Thesis (Ph. D.)--University of Missouri-Columbia, 1997. / Typescript. Vita. Includes bibliographical references (leaves 119-128). Also available on the Internet.

Thesis (Ph.D)--Electrical and Computer Engineering, Georgia Institute of Technology, 2010. / Committee Chair: Thomas K. Gaylord; Committee Member: Donald D. Davis; Committee Member: Gee-Kung Chang; Committee Member: Muhannad S. Bakir; Committee Member: Phillip N. First. Part of the SMARTech Electronic Thesis and Dissertation Collection.

Thesis (Ph. D.)--University of Chicago, Dept. of Geophysical Sciences, August 1999. / Includes bibliographical references. Also available on the Internet.