A Multidimensional Discontinuous Galerkin Modeling Framework For Overland Flow And Channel Routing

This thesis presents the development and application of a multidimensional (2-D & 1-D) kinematic wave model in a discontinuous Galerkin framework for simulating overland flow and runoff due to torrential rainfall. The objective of this work is to improve on (1) the modeling approach involving many small-scale rivers and channels and (2) the accuracy of flooding caused by storm surge coupled with torrential rainfall. The overland flow is modeled using the 2-D kinematic wave equations derived from the 2-D depth averaged shallow water equations. In areas of the domain where flow converges into channels, the edges of 2-D elements are used as 1-D channels for flow routing. To best represent complex topography, domains are discretized using an application co-developed by the author called Admesh+, an automatic unstructured mesh generator for shallow water models. Admesh+ produces high-quality meshes with the appropriate amount of refinement where it is needed to resolve all of the geometry and flow characteristics of the domain. The mesh generation technique utilizes high-resolution digital elevation maps (DEMs) to automatically produce unstructured meshes with elements arranged to best represent shorelines, channel networks and watershed delineations. The development of the multidimensional overland flow model and mesh generation techniques are presented along with comparisons of model results with various analytic solutions and experimental data.

The issue of local scale and smoothness presents a crucial and daunting challenge for numerical simulation methods in fluid dynamics. Yet in the interests of both accuracy and economy, how can one devise a general technique that efficiently resolves flow features of consequence and discriminates against others which are either ``negligible' or amenable to ``universal' modeling? This is particularly difficult because geometries of engineering interest are complex and multi-dimensional, precluding a priori knowledge of the flowfield. To address this challenge, the current work employs wavelet theory for the local scale decomposition of functions, which provides a natural mechanism for the adaptive compression of data. The resulting technique is known as the Multi-Resolution Discontinuous Galerkin (MRDG) method.

This edited review book on Godunov methods contains 97 articles, all of which were presented at the international conference on Godunov Methods: Theory and Applications, held at Oxford in October 1999, to commemo rate the 70th birthday of the Russian mathematician Sergei K. Godunov. The meeting enjoyed the participation of 140 scientists from 20 countries; one of the participants commented: everyone is here, meaning that virtu ally everybody who had made a significant contribution to the general area of numerical methods for hyperbolic conservation laws, along the lines first proposed by Godunov in the fifties, was present at the meeting. Sadly, there were important absentees, who due to personal circumstance could not at tend this very exciting gathering. The central theme o{ the meeting, and of this book, was numerical methods for hyperbolic conservation laws fol lowing Godunov's key ideas contained in his celebrated paper of 1959. But Godunov's contributions to science are not restricted to Godunov's method.

The breakup of a river ice cover can be both fascinating and perilous, owing to ever-changing ice conditions and dynamic processes that sometimes lead to extreme flood events caused by ice jams. Though much progress has been made recently in the study of ice jams, less has been achieved on the more general, and more complex, problem of how to predict the entire breakup process, from the first ice movement to the last ice effect on river stage. This type of knowledge is essential to determining when and where ice jam threats may develop and when they may release and generate steep flood waves that can trigger ice runs and jamming further downstream. In turn, such understanding is invaluable to natural hazard reduction, ecosystem conservation and protection, and adaptation to climatic impacts. This book combines the existing information, previously scattered in various journals, conference proceedings, and technical reports. It contains contributions by several authors to achieve a comprehensive and balanced coverage, including qualitative and quantitative descriptions of relevant physical processes, forecasting methods and flood-frequency assessments, as well as ecological impacts and climatic considerations. The book should be of interest to readers of different backgrounds, both beginners and specialists. -- Publisher's website.

This book focuses on motions of incompressible ?uids of a freely moving surface being in?uenced by both the Earth’s rotation and density strati?cation. In contrast to traditional textbooks in the ?eld of geophysical ?uid dynamics, such as those by by Cushman-Roisin (1994) and Gill (1982), this book uses the method of proce- oriented hydrodynamic modelling to illustrate a rich variety of ?uid phenomena. To this end, the reader can adopt the model codes, found on the Springer server accompanying this book, to reproduce most graphs of this book and, even better, to create animation movies. The reader can also employ the codes as templates for own independent studies. This can be done by a lay person as a hobby activity, undergraduate or postgraduate students as part of their education, or professional scientists as part of research. Exercises of this book are run with open-source software that can be freely downloaded from the Internet. This includes the FORTRAN 95 compiler “G95” used for execution of model simulations, the data visualisation program “SciLab”, and “ImageMagick” for the creation of graphs and GIF animations, which can be watched with most Internet browsers.

This book provides a systematic treatment of the geometrical and transport properties of fractures, fracture networks, and fractured porous media. It is divided into two major parts. The first part deals with geometry of individual fractures and of fracture networks. The use of the dimensionless density rationalizes the results for the percolation threshold of the networks. It presents the crucial advantage of grouping the numerical data for various fracture shapes. The second part deals mainly with permeability under steady conditions of fractures, fracture networks, and fractured porous media. Again the results for various types of networks can be rationalized by means of the dimensionless density. A chapter is dedicated to two phase flow in fractured porous media.

Computational Hydraulics introduces the concept of modeling and the contribution of numerical methods and numerical analysis to modeling. It provides a concise and comprehensive description of the basic hydraulic principles, and the problems addressed by these principles in the aquatic environment. Flow equations, numerical and analytical solutions are included. The necessary steps for building and applying numerical methods in hydraulics comprise the core of the book and this is followed by a report of different example applications of computational hydraulics: river training effects on flood propagation, water quality modelling of lakes and coastal applications. The theory and exercises included in the book promote learning of concepts within academic environments. Sample codes are made available online for purchasers of the book. Computational Hydraulics is intended for under-graduate and graduate students, researchers, members of governmental and non-governmental agencies and professionals involved in management of the water related problems. Author: Ioana Popescu, Hydroinformatics group, UNESCO-IHE Institute for Water Education, Delft , The Netherlands.

Written by the leading experts in computational materials science, this handy reference concisely reviews the most important aspects of plasticity modeling: constitutive laws, phase transformations, texture methods, continuum approaches and damage mechanisms. As a result, it provides the knowledge needed to avoid failures in critical systems udner mechanical load. With its various application examples to micro- and macrostructure mechanics, this is an invaluable resource for mechanical engineers as well as for researchers wanting to improve on this method and extend its outreach.

The LES-method is rapidly developing in many practical applications in engineering The mathematical background is presented here for the first time in book form by one of the leaders in the field

First published in 1957, this is a classic monograph in the area of applied mathematics. It offers a connected account of the mathematical theory of wave motion in a liquid with a free surface and subjected to gravitational and other forces, together with applications to a wide variety of concrete physical problems. A never-surpassed text, it remains of permanent value to a wide range of scientists and engineers concerned with problems in fluid mechanics. The four-part treatment begins with a presentation of the derivation of the basic hydrodynamic theory for non-viscous incompressible fluids and a description of the two principal approximate theories that form the basis for the rest of the book. The second section centers on the approximate theory that results from small-amplitude wave motions. A consideration of problems involving waves in shallow water follows, and the text concludes with a selection of problems solved in terms of the exact theory. Despite the diversity of its topics, this text offers a unified, readable, and largely self-contained treatment.