Doctor of Philosophy

dissertationOne of the fundamental building blocks of many computational sciences is the construction and use of a discretized, geometric representation of a problem domain, often referred to as a mesh. Such a discretization enables an otherwise complex domain to be represented simply, and computation to be performed over that domain with a finite number of basis elements. As mesh generation techniques have become more sophisticated over the years, focus has largely shifted to quality mesh generation techniques that guarantee or empirically generate numerically well-behaved elements. In this dissertation, the two complementary meshing subproblems of vertex placement and element creation are analyzed, both separately and together. First, a dynamic particle system achieves adaptivity over domains by inferring feature size through a new information passing algorithm. Second, a new tetrahedral algorithm is constructed that carefully combines lattice-based stenciling and mesh warping to produce guaranteed quality meshes on multimaterial volumetric domains. Finally, the ideas of lattice cleaving and dynamic particle systems are merged into a unified framework for producing guaranteed quality, unstructured and adaptive meshing of multimaterial volumetric domains

Error estimation for simplifications of electrostatic models

Based on a posteriori error estimation a method to bound the error induced by simplifying the geometry of a model is presented. Error here refers to the solution of a partial differential equation and a specific quantity of interest derived from it. Geometry simplification specifically refers to replacing CAD model features with simpler shapes. The simplification error estimate helps to determine whether a feature can be removed from the model by indicating how much the simplification affects the physical properties of the model as measured by a quantity of interest. The approach in general can also be extended to other problems governed by linear elliptic equations. Strict bounds for the error are proven for errors expressed in the energy norm. The approach relies on the Constitutive Relation Error to enable practically useful and computationally affordable bounds for error measures in the energy error norm. All methodologies are demonstrated for a second order elliptic partial differential equation for electrostatic problems. Finite element simplification error estimation code is developed to calculate the simplification error numerically. Numerical experiments for some geometric models of capacitors show satisfactory results for the simplification error bounds for a range of different deafeaturing cases and a quantity of interest, linear in the solution of the electrostatic partial differential equation. Overall the numerically calculated bounds are always valid, but are more or less accurate depending on the type of feature and its simplification. In particular larger errors may be overestimated, while good estimates for small errors can be achieved. This makes the bound overall suitable to decide whether simplifying a feature is acceptable or not

Adaptive modelling in atomistic-to-continuum multiscale methods

International audienceDue to the lack of computational power to perform a fully atomistic simulation of practical, engineering systems, a number of concurrent multiscale methods is developed to limit atomic model to a small cluster of atoms near the hot spot. In this paper the overview of salient features of the main multiscale families is given. The special attention is drawn towards the role of model adaptivity, that is, which part of the problem domain to model by the atomic scale (the hot spot) and which by coarse scale model, as well as where to place the interface of the two models to control the accuracy. Taking Quasicontinuum method as a reference, review of the evolution of the Bridging domain/Arlequin method is given, which parallels the development of a posteriori modeling error estimation

Modeling of Electrokinetic Mixing in Lab on Chip Microfluidic Devices

This dissertation summarize a modeling of electrokinetic mixing employing electro-osmotic stationary and time-dependent micropumps via alternate zeta potential patches on the lower surface of the mixing chamber in lab on chip microfluidic device. Electro-osmotic flow is augmented using different model designs with alternate zeta potential values such as 25mV, 50mV and 100mV respectively to achieve high mixing efficiency in electrokinetically driven microfluidic system. The enhancement of mixing via alternate opposing zeta potentials is studied using Finite Element Modeling. Simulation 2D and 3D workflow involves designated steps such as setting up the model environment, creating geometric objects, stipulating materials and boundary conditions, meshing and post analyzing the results. An electric contours and concentration gradients are derived using a Navier-Stokes for incompressible flow, convection-diffusion equation and Helmholtz-Smoluchowski slip velocity respectively. The effect of magnitude of zeta potential, number of alternate patches etc. are studied in detail. In addition, 2D results are compared with 3D results to demonstrate the significance of 3D model in microfluidic design process

An interface tracking model for droplet electrocoalescence.

This report describes an Early Career Laboratory Directed Research and Development (LDRD) project to develop an interface tracking model for droplet electrocoalescence. Many fluid-based technologies rely on electrical fields to control the motion of droplets, e.g. microfluidic devices for high-speed droplet sorting, solution separation for chemical detectors, and purification of biodiesel fuel. Precise control over droplets is crucial to these applications. However, electric fields can induce complex and unpredictable fluid dynamics. Recent experiments (Ristenpart et al. 2009) have demonstrated that oppositely charged droplets bounce rather than coalesce in the presence of strong electric fields. A transient aqueous bridge forms between approaching drops prior to pinch-off. This observation applies to many types of fluids, but neither theory nor experiments have been able to offer a satisfactory explanation. Analytic hydrodynamic approximations for interfaces become invalid near coalescence, and therefore detailed numerical simulations are necessary. This is a computationally challenging problem that involves tracking a moving interface and solving complex multi-physics and multi-scale dynamics, which are beyond the capabilities of most state-of-the-art simulations. An interface-tracking model for electro-coalescence can provide a new perspective to a variety of applications in which interfacial physics are coupled with electrodynamics, including electro-osmosis, fabrication of microelectronics, fuel atomization, oil dehydration, nuclear waste reprocessing and solution separation for chemical detectors. We present a conformal decomposition finite element (CDFEM) interface-tracking method for the electrohydrodynamics of two-phase flow to demonstrate electro-coalescence. CDFEM is a sharp interface method that decomposes elements along fluid-fluid boundaries and uses a level set function to represent the interface