An environmental magnetic study, sedimentological and numerical methods around Tauranga Harbour, New Zealand

Magnetic iron minerals are widespread and indicative sediment constituents in estuarine, coastal and shelf systems. We combine environmental magnetic, sedimentological and numerical methods to identify magnetite-enriched placer-like zones in a complex coastal system and delineate their formation mechanisms. Magnetic susceptibility and remanence measurements on 245 surficial sediment samples collected in and around Tauranga Harbour, the largest barrier-enclosed tidal estuary of New Zealand, reveal several discrete enrichment zones controlled by local hydrodynamic conditions. Active magnetite enrichment takes place in tidal channels, which feed into two coast-parallel nearshore magnetite-enriched belts centered at water depths of 6-10 m and 10-20 m. A close correlation between magnetite content and magnetic grain size was found, where higher susceptibility values are associated within coarser magnetic crystal sizes. Two key mechanisms for magnetite enrichment are identified. First, tide-induced residual currents primarily enable magnetite enrichment within the estuarine channel network. A coast-parallel, fine sand magnetite enrichment belt in water depths of less than 10 m along the barrier island has a strong decrease in magnetite content away from the southern tidal inlet and is apparently related to active coast-parallel transport combined with mobilizing surf zone processes. A second, less pronounced, but more uniform magnetite enrichment belt at 10-20 m water depth is composed of non-mobile, medium-coarse-grained relict sands, which have been reworked during post-glacial sea level transgression. We demonstrate the potential of magnetic methods to reveal and differentiate coastal magnetite enrichment patterns and investigate their formative mechanisms.

Coupling time-stepping numerical methods and standard aerodynamics codes for instability analysis of flows in complex geometries

The development of a global instability analysis code coupling a time-stepping approach, as applied to the solution of BiGlobal and TriGlobal instability analysis 1, 2 and ���nite-volume-based spatial discretization, as used in standard aerodynamics codes is presented. The key advantage of the time-stepping method over matrix-formulation approaches is that the former provides a solution to the computer-storage issues associated with the latter methodology. To-date both approaches are successfully in use to analyze instability in complex geometries, although their relative advantages have never been quanti���ed. The ultimate goal of the present work is to address this issue in the context of spatial discretization schemes typically used in industry. The time-stepping approach of Chiba 3 has been implemented in conjunction with two direct numerical simulation algorithms, one based on the typically-used in this context high-order method and another based on low-order methods representative of those in common use in industry. The two codes have been validated with solutions of the BiGlobal EVP and it has been showed that small errors in the base ���ow do not have a���ect signi���cantly the results. As a result, a three-dimensional compressible unsteady second-order code for global linear stability has been successfully developed based on ���nite-volume spatial discretization and time-stepping method with the ability to study complex geometries by means of unstructured and hybrid meshes

Efficient numerical methods for global linear instability. Analysis and modeling of non-orthogonal swept attachment-line boundary layer flow

The aim of this thesis is to study the mechanisms of instability that occur in swept wings when the angle of attack increases. For this, a simplified model for the a simplified model for the non-orthogonal swept leading edge boundary layer has been used as well as different numerical techniques in order to solve the linear stability problem that describes the behavior of perturbations superposed upon this base flow. Two different approaches, matrix-free and matrix forming methods, have been validated using direct numerical simulations with spectral resolution. In this way, flow instability in the non-orthogonal swept attachment-line boundary layer is addressed in a linear analysis framework via the solution of the pertinent global (Bi-Global) PDE-based eigenvalue problem. Subsequently, a simple extension of the extended G��ortler-H��ammerlin ODEbased polynomial model proposed by Theofilis, Fedorov, Obrist & Dallmann (2003) for orthogonal flow, which includes previous models as particular cases and recovers global instability analysis results, is presented for non-orthogonal flow. Direct numerical simulations have been used to verify the stability results and unravel the limits of validity of the basic flow model analyzed. The effect of the angle of attack, AoA, on the critical conditions of the non-orthogonal problem has been documented; an increase of the angle of attack, from AoA = 0 (orthogonal flow) up to values close to _/2 which make the assumptions under which the basic flow is derived questionable, is found to systematically destabilize the flow. The critical conditions of non-orthogonal flows at 0 _ AoA _ _/2 are shown to be recoverable from those of orthogonal flow, via a simple analytical transformation involving AoA. These results can help to understand the mechanisms of destabilization that occurs in the attachment line of wings at finite angles of attack. Studies taking into account variations of the pressure field in the basic flow or the extension to compressible flows are issues that remain open. El objetivo de esta tesis es estudiar los mecanismos de la inestabilidad que se producen en ciertos dispositivos aerodin��micos cuando se aumenta el ��ngulo de ataque. Para ello se ha utilizado un modelo simplificado del flujo de base, as�� como diferentes t��cnicas num��ricas, con el fin de resolver el problema de estabilidad lineal asociado que describe el comportamiento de las perturbaciones. Estos m��todos; sin y con formaci��n de matriz, se han validado utilizando simulaciones num��ricas directas con resoluci��n espectral. De esta manera, la inestabilidad del flujo de capa l��mite laminar oblicuo entorno a la l��nea de estancamiento se aborda en un marco de an��lisis lineal por medio del m��todo Bi-Global de resoluci��n del problema de valores propios en derivadas parciales. Posteriormente se propone una extensi��n simple para el flujo no-ortogonal del modelo polinomial de ecuaciones diferenciales ordinarias, G��ortler-H��ammerlin extendido, propuesto por Theofilis et al. (2003) para el flujo ortogonal, que incluye los modelos previos como casos particulares y recupera los resultados del analisis global de estabilidad lineal. Se han realizado simulaciones directas con el fin de verificar los resultados del an��lisis de estabilidad as�� como para investigar los l��mites de validez del modelo de flujo base utilizado. En este trabajo se ha documentado el efecto del ��ngulo de ataque AoA en las condiciones cr��ticas del problema no ortogonal obteniendo que el incremento del ��ngulo de ataque, de AoA = 0 (flujo ortogonal) hasta valores pr��ximos a _/2, en el cual las hip��tesis sobre las que se basa el flujo base dejan de ser v��lidas, tiende sistem��ticamente a desestabilizar el flujo. Las condiciones cr��ticas del caso no ortogonal 0 _ AoA _ _/2 pueden recuperarse a partir del caso ortogonal mediante el uso de una transformaci��n anal��tica simple que implica el ��ngulo de ataque AoA. Estos resultados pueden ayudar a comprender los mecanismos de desestabilizaci��n que se producen en el borde de ataque de las alas de los aviones a ��ngulos de ataque finitos. Como tareas pendientes quedar��a realizar estudios que tengan en cuenta variaciones del campo de presi��n en el flujo base as�� como la extensi��n de ��ste al caso de flujos compresibles.

Numerical methods for option pricing.

This thesis aims to introduce some fundamental concepts underlying option valuation theory including implementation of computational tools. In many cases analytical solution for option pricing does not exist, thus the following numerical methods are used: binomial trees, Monte Carlo simulations and finite difference methods. First, an algorithm based on Hull and Wilmott is written for every method. Then these algorithms are improved in different ways. For the binomial tree both speed and memory usage is significantly improved by using only one vector instead of a whole price storing matrix. Computational time in Monte Carlo simulations is reduced by implementing a parallel algorithm (in C) which is capable of improving speed by a factor which equals the number of processors used. Furthermore, MatLab code for Monte Carlo was made faster by vectorizing simulation process. Finally, obtained option values are compared to those obtained with popular finite difference methods, and it is discussed which of the algorithms is more appropriate for which purpose.

Numerical methods in Nonlinear Analysis of shell structures

The design of shell and spatial structures represents an important challenge even with the use of the modern computer technology.If we concentrate in the concrete shell structures many problems must be faced,such as the conceptual and structural disposition, optimal shape design, analysis, construction methods, details etc. and all these problems are interconnected among them. As an example the shape optimization requires the use of several disciplines like structural analysis, sensitivity analysis, optimization strategies and geometrical design concepts. Similar comments can be applied to other space structures such as steel trusses with single or double shape and tension structures. In relation to the analysis the Finite Element Method appears to be the most extended and versatile technique used in the practice. In the application of this method several issues arise. First the derivation of the pertinent shell theory or alternatively the degenerated 3-D solid approach should be chosen. According to the previous election the suitable FE model has to be adopted i.e. the displacement,stress or mixed formulated element. The good behavior of the shell structures under dead loads that are carried out towards the supports by mainly compressive stresses is impaired by the high imperfection sensitivity usually exhibited by these structures. This last effect is important particularly if large deformation and material nonlinearities of the shell may interact unfavorably, as can be the case for thin reinforced shells. In this respect the study of the stability of the shell represents a compulsory step in the analysis. Therefore there are currently very active fields of research such as the different descriptions of consistent nonlinear shell models given by Simo, Fox and Rifai, Mantzenmiller and Buchter and Ramm among others, the consistent formulation of efficient tangent stiffness as the one presented by Ortiz and Schweizerhof and Wringgers, with application to concrete shells exhibiting creep behavior given by Scordelis and coworkers; and finally the development of numerical techniques needed to trace the nonlinear response of the structure. The objective of this paper is concentrated in the last research aspect i.e. in the presentation of a state-of-the-art on the existing solution techniques for nonlinear analysis of structures. In this presentation the following excellent reviews on this subject will be mainly used.

Problems for the numerical analysis of the future; [papers presented at the symposium on modern calculating machinery and numerical methods, held on July 29-31, 1948, at the University of California, Los Angeles]

Includes bibliographies.

A computer graphic technique for finding numerical methods for ordinary differential equations.

On cover: COO-1469-0106.

Multi-derivative numerical methods for the solution of stiff ordinary differential equations /

"Under contracts US AEC AT(11-1)2383 and US AEC AT(11-1)1469."

Numerical methods for the identification of differential equations,

Thesis - University of Illinois at Urbana-Champaign.

Power spectrum measurements by numerical methods. Internal research project 85-440.

Mode of access: Internet.

Modeling collisional processes in plasmas using discontinuous numerical methods

Thesis (Ph.D.)--University of Washington, 2016-06

Numerical methods for strong solutions of stochastic differential equations: an overview

This paper gives a review of recent progress in the design of numerical methods for computing the trajectories (sample paths) of solutions to stochastic differential equations. We give a brief survey of the area focusing on a number of application areas where approximations to strong solutions are important, with a particular focus on computational biology applications, and give the necessary analytical tools for understanding some of the important concepts associated with stochastic processes. We present the stochastic Taylor series expansion as the fundamental mechanism for constructing effective numerical methods, give general results that relate local and global order of convergence and mention the Magnus expansion as a mechanism for designing methods that preserve the underlying structure of the problem. We also present various classes of explicit and implicit methods for strong solutions, based on the underlying structure of the problem. Finally, we discuss implementation issues relating to maintaining the Brownian path, efficient simulation of stochastic integrals and variable-step-size implementations based on various types of control.