Numerical Analysis and Computation Commons^™

Novel Approaches To Compute Manifold Operators With The Radial Basis Functions Method, Jacob James Blazejewski

Dissertations, Master's Theses and Master's Reports

The bulk of this dissertation is mainly composed of four chapters, which are organized as follows: Chapter 1 provides an introduction to the Radial Basis Functions (RBF) method by briefly outlining its historical developments and reviewing the RBF interpolation and the RBF-Finite Difference (FD) methodologies, and their advantages/disadvantages. Chapter 2 describes the Orthogonal Gradients (OGr) method and the Fast OGr method and how these can be used to compute differential operators restricted to hypersurfaces and space curves ($\Gamma$) embedded in R3. We will highlight a challenge of pairing Fast OGr with RBF-FD on nearly flat local clusters and how to …

Improving The Temporal Accuracy Of Turbulence Models And Resolving The Implementation Issues Of Fluid Flow Modeling, Kyle J. Schwiebert

Dissertations, Master's Theses and Master's Reports

A sizeable proportion of the work in this thesis focuses on a new turbulence model, dubbed ADC (the approximate deconvolution model with defect correction). The ADC is improved upon using spectral deferred correction, a means of constructing a higher order ODE solver. Since both the ADC and SDC are based on a predictor-corrector approach, SDC is incorporated with essentially no additional computational cost. We will show theoretically and using numerical tests that the new scheme is indeed higher order in time than the original, and that the benefits of defect correction, on which the ADC is based, are preserved.

The …

Deterministic And Statistical Methods For Inverse Problems With Partial Data, Yanfang Liu

Dissertations, Master's Theses and Master's Reports

Inverse problems with partial data have many applications in science and engineering. They are more challenging than the complete data cases since the lack of data increases ill-posedness and nonlinearity. The use of only deterministic or statistical methods might not provide satisfactory results. We propose to combine the deterministic and statistical methods to treat such inverse problems. The thesis is organized as follows.

In Chapter 1, we briefly introduce the inverse problems and their applications. The classical deterministic methods and Bayesian inversion are discussed. The chapter is concluded with a summary of contributions.

Chapter 2 considers the reconstruction of the …

Higher Accuracy Methods For Fluid Flows In Various Applications: Theory And Implementation, Dilek Erkmen

Dissertations, Master's Theses and Master's Reports

This dissertation contains research on several topics related to Defect-deferred correction (DDC) method applying to CFD problems. First, we want to improve the error due to temporal discretization for the problem of two convection dominated convection-diffusion problems, coupled across a joint interface. This serves as a step towards investigating an atmosphere-ocean coupling problem with the interface condition that allows for the exchange of energies between the domains.

The main diffuculty is to decouple the problem in an unconditionally stable way for using legacy code for subdomains. To overcome the issue, we apply the Deferred Correction (DC) method. The DC method …

Discontinuous Galerkin Methods For Convection-Diffusion Equations And Applications In Petroleum Engineering, Nattaporn Chuenjarern

Dissertations, Master's Theses and Master's Reports

This dissertation contains research in discontinuous Galerkin (DG) methods applying to convection-diffusion equations. It contains both theoretical analysis and applications. Initially, we develop a conservative local discontinuous Galerkin (LDG) method for the coupled system of compressible miscible displacement problem in two space dimensions. The main difficulty is how to deal with the discontinuity of approximations of velocity, u, in the convection term across the cell interfaces. To overcome the problems, we apply the idea of LDG with IMEX time marching using the diffusion term to control the convection term. Optimal error estimates in L^infinity(0, T; L^{2 …}

Approximation Of The Generalized Singular Value Expansion, Matthew Jacob Roberts

Dissertations, Master's Theses and Master's Reports

Let $X$, $Y$, and $Z$ be real separable Hilbert spaces, let $T:X \to Y$ be a compact operator, and let $L:D(L) \to Z$ be a closed and densely defined linear operator. Then the generalized singular value expansion (GSVE) is an expansion that expresses $T$ and $L$ in terms of a common orthonormal basis. Under certain hypotheses on discretization, the GSVE of an approximate operator pair $(T_j,L_j)$, where $T_j:X_j \to Y_j$ and $L_j:X_j \to Z_j$, converges to the GSVE of $(T,L)$. Error estimates establish a rate of convergence that is consistent with numerical experiments in the case of discretization using piecewise …

High Order Bound-Preserving Discontinuous Galerkin Methods And Their Applications In Petroleum Engineering, Ziyao Xu

Dissertations, Master's Theses and Master's Reports

This report contains researches in the theory of high-order bound-preserving (BP) discontinuous Galerkin (DG) method and their applications in petroleum engineering. It contains both theoretical analysis and numerical experiments. The compressible miscible displacements and wormhole propagation problem, arising in petroleum engineering, is used to describe the evolution of the pressure and concentrations of different components of fluid in porous media. The important physical features of concentration and porosity include their boundedness between 0 and 1, as well as the monotone increasing for porosity in wormhole propagation model. How to keep these properties in the simulation is crucial to the robustness …

A Model To Predict Concentrations And Uncertainty For Mercury Species In Lakes, Ashley Hendricks

Dissertations, Master's Theses and Master's Reports

To increase understanding of mercury cycling, a seasonal mass balance model was developed to predict mercury concentrations in lakes and fish. Results indicate that seasonality in mercury cycling is significant and is important for a northern latitude lake. Models, when validated, have the potential to be used as an alternative to measurements; models are relatively inexpensive and are not as time intensive. Previously published mercury models have neglected to perform a thorough validation. Model validation allows for regulators to be able to make more informed, confident decisions when using models in water quality management. It is critical to quantify uncertainty; …

Evaporation Of A Sessile Droplet On A Slope, Mitch Timm

Dissertations, Master's Theses and Master's Reports

We theoretically examine the drying of a stationary liquid droplet on an inclined surface. Both analytical and numerical approaches are considered, while assuming that the evaporation results from a purely diffusive transport of the liquid vapor and that the contact line is a pinned circle. For the purposes of our analytical calculations, we suppose that the effect of gravity relative to the surface tension is weak, i.e. the Bond number (Bo) is small. Then, we express the shape of the drop and the vapor concentration field as perturbation expansions in terms of Bo. When the Bond number is zero, the …

High Accuracy Methods And Regularization Techniques For Fluid Flows And Fluid-Fluid Interaction, Mustafa Aggul

Dissertations, Master's Theses and Master's Reports

This dissertation contains several approaches to resolve irregularity issues of CFD problems, including a decoupling of non-linearly coupled fluid-fluid interaction, due to high Reynolds number. New models present not only regularize the linear systems but also produce high accurate solutions both in space and time. To achieve this goal, methods solve a computationally attractive artificial viscosity approximation of the target problem, and then utilize a correction approach to make it high order accurate. This way, they all allow the usage of legacy code | a frequent requirement in the simulation of fluid flows in complex geometries. In addition, they all …

Pseudo-Companion Matrices For Polynomial Systems, Melinda Kleczynski

Dissertations, Master's Theses and Master's Reports

Roots of a scalar polynomial in one variable are frequently found by computing the eigenvalues of the standard companion matrix. In this exploratory work, we introduce the pseudo-companion matrix for finding roots of multivariable polynomial systems. In some cases, a perturbation of the polynomial system is used for the matrix construction, yielding approximate roots of the original polynomial system. The coordinates of the roots, or their approximations, are obtained from the eigenvectors of this matrix. In this thesis, we describe the process of constructing the pseudo-companion matrix and computing the polynomial roots using illustrative examples.

Wildfire Emissions In The Context Of Global Change And The Implications For Mercury Pollution, Aditya Kumar

Dissertations, Master's Theses and Master's Reports

Wildfires are episodic disturbances that exert a significant influence on the Earth system. They emit substantial amounts of atmospheric pollutants, which can impact atmospheric chemistry/composition and the Earth’s climate at the global and regional scales. This work presents a collection of studies aimed at better estimating wildfire emissions of atmospheric pollutants, quantifying their impacts on remote ecosystems and determining the implications of 2000s-2050s global environmental change (land use/land cover, climate) for wildfire emissions following the Intergovernmental Panel on Climate Change (IPCC) A1B socioeconomic scenario.

A global fire emissions model is developed to compile global wildfire emission inventories for major atmospheric …

Modeling And Simulation Of The Peristaltic Flow Of Newtonian And Non-Newtonian Fluids With Application To The Human Body, Samer Alokaily

Dissertations, Master's Theses and Master's Reports

Computational models are developed to investigate peristaltic motion in the human gastro-intestinal tract. The peristaltic motion is simulated by means of traveling waves which deform the boundary of the tubes. An axisymmetric tube of uniform diameter is used to model the small intestines, and an axisymmetric conical geometry is developed to model the lower part of the human stomach. The conical geometry represents a simplification of the more complicated three-dimensional models of the human stomach that have been used in other studies. Also, they seeks to reduce computational costs and circumvent difficulties of mesh generation. The computations are performed within …

Numerical Simulation Of Viscoelastic Multiphase Flows Using An Improved Two-Phase Flow Solver, Olabanji Shonibare

Dissertations, Master's Theses and Master's Reports

The production of uniformly-sized droplets has numerous applications in various fields including the biotechnology and chemical industries. For example, in the separation of mixtures based on their relative absorbency, an optimal arrangement of monodispersed droplets in columns is desired for an effective separation. However, very few numerical studies on the formation of viscoelastic droplets via cross-flow shear are available, none of which have considered the case when the flow of the continuous phase is Couette. In this work, a new solver capable of automatic mesh refinement is developed for the OpenFOAM CFD toolbox to solve viscoelastic two-phase flow problems. The …

Direct Sampling Methods For Inverse Scattering Problems, Ala Mahmood Nahar Al Zaalig

Dissertations, Master's Theses and Master's Reports

Recently, direct sampling methods became popular for solving inverse scattering problems to estimate the shape of the scattering object. They provide a simple tool to directly reconstruct the shape of the unknown scatterer. These methods are based on choosing an appropriate indicator function f on R^d, d=2 or 3, such that f(z) decides whether z lies inside or outside the scatterer. Consequently, we can determine the location and the shape of the unknown scatterer.

In this thesis, we first present some sampling methods for shape reconstruction in inverse scattering problems. These methods, which are described in Chapter 1, …

Methodology For Analyzing Epoxy-Cnt Phononic Crystals For Wave Attenuation And Guiding, Madhu Kolati

Dissertations, Master's Theses and Master's Reports

Phononic crystals (PhnCs) control, direct and manipulate sound waves to achieve wave guiding and attenuation. This dissertation presents methodology for analyzing nanotube materials based phononic crystals to achieve control over sound, vibration and stress mitigation. Much of the analytical work presented is in identifying frequency band gaps in which sound or vibration cannot propagate through these PhnCs. Wave attenuation and mitigation analysis is demonstrated using finite element simulation. Engineering principles from current research areas of solid mechanics, solid-state physics, elasto-dynamics, mechanical vibrations and acoustics are employed for the methodology. A considerable effort is put to show that these PhnCs can …

Defect-Deferred Correction Method For The Two-Domain Convection-Dominated Convection-Diffusion Problem, Dilek Erkmen

Dissertations, Master's Theses and Master's Reports

We present a method for solving a fluid-fluid interaction problem (two convection-dominated convection-diusion problems adjoined by an interface), which is a simplifed version of the atmosphere ocean coupling problem. The method resolves some of the issues that can be crucial to the fluid-fluid interaction problems: it is a partitioned time stepping method, yet it is of high order accuracy in both space and time (the two-step algorithm considered in this report provides second order accuracy); it allows for the usage of the legacy codes (which is a common requirement when resolving flows in complex geometries), yet it can be applied …

A High Accuracy Minimally Invasive Regularization Technique For Navier-Stokes Equations At High Reynolds Number, Mustafa Aggul

Dissertations, Master's Theses and Master's Reports

A method is presented, that combines the defect and deferred correction approaches to approximate solutions of Navier-Stokes equations at high Reynolds number. The method is of high accuracy in both space and time, and it allows for the usage of legacy codes (a frequent requirement in the simulation of turbulent flows in complex geometries). The two-step method is considered here; in order to obtain a regularization that is second order accurate in space and time, the method computes a low-order accurate, stable and computationally inexpensive approximation (Backward Euler with artificial viscosity) twice. The results are readily extendable to the higher …