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Multiscale Basis Optimization For Darcy Flow
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Book Synopsis Multiscale Basis Optimization for Darcy Flow by : James Michael Rath
Download or read book Multiscale Basis Optimization for Darcy Flow written by James Michael Rath and published by . This book was released on 2007 with total page 91 pages. Available in PDF, EPUB and Kindle. Book excerpt: Simulation of flow through a heterogeneous porous medium with fine-scale features can be computationally expensive if the flow is fully resolved. Coarsening the problem gives a faster approximation of the flow but loses some detail. We propose an algorithm that obtains the fully resolved approximation but only iterates on a sequence of coarsened problems. The sequence is chosen by optimizing the shapes of the coarse finite element basis functions.
Book Synopsis Numerical Analysis of Multiscale Problems by : Ivan G. Graham
Download or read book Numerical Analysis of Multiscale Problems written by Ivan G. Graham and published by Springer Science & Business Media. This book was released on 2012-01-05 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 91st London Mathematical Society Durham Symposium took place from July 5th to 15th 2010, with more than 100 international participants attending. The Symposium focused on Numerical Analysis of Multiscale Problems and this book contains 10 invited articles from some of the meeting's key speakers, covering a range of topics of contemporary interest in this area. Articles cover the analysis of forward and inverse PDE problems in heterogeneous media, high-frequency wave propagation, atomistic-continuum modeling and high-dimensional problems arising in modeling uncertainty. Novel upscaling and preconditioning techniques, as well as applications to turbulent multi-phase flow, and to problems of current interest in materials science are all addressed. As such this book presents the current state-of-the-art in the numerical analysis of multiscale problems and will be of interest to both practitioners and mathematicians working in those fields.
Book Synopsis Multiscale Optimization Methods and Applications by : William W. Hager
Download or read book Multiscale Optimization Methods and Applications written by William W. Hager and published by Springer Science & Business Media. This book was released on 2006-06-18 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: As optimization researchers tackle larger and larger problems, scale interactions play an increasingly important role. One general strategy for dealing with a large or difficult problem is to partition it into smaller ones, which are hopefully much easier to solve, and then work backwards towards the solution of original problem, using a solution from a previous level as a starting guess at the next level. This volume contains 22 chapters highlighting some recent research. The topics of the chapters selected for this volume are focused on the development of new solution methodologies, including general multilevel solution techniques, for tackling difficult, large-scale optimization problems that arise in science and industry. Applications presented in the book include but are not limited to the circuit placement problem in VLSI design, a wireless sensor location problem, optimal dosages in the treatment of cancer by radiation therapy, and facility location.
Book Synopsis Flow and Transport in Porous Media and Fractured Rock by : Muhammad Sahimi
Download or read book Flow and Transport in Porous Media and Fractured Rock written by Muhammad Sahimi and published by John Wiley & Sons. This book was released on 2011-05-09 with total page 635 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this standard reference of the field, theoretical and experimental approaches to flow, hydrodynamic dispersion, and miscible displacements in porous media and fractured rock are considered. Two different approaches are discussed and contrasted with each other. The first approach is based on the classical equations of flow and transport, called 'continuum models'. The second approach is based on modern methods of statistical physics of disordered media; that is, on 'discrete models', which have become increasingly popular over the past 15 years. The book is unique in its scope, since (1) there is currently no book that compares the two approaches, and covers all important aspects of porous media problems; and (2) includes discussion of fractured rocks, which so far has been treated as a separate subject. Portions of the book would be suitable for an advanced undergraduate course. The book will be ideal for graduate courses on the subject, and can be used by chemical, petroleum, civil, environmental engineers, and geologists, as well as physicists, applied physicist and allied scientists that deal with various porous media problems.
Book Synopsis Multiscale Analysis and Computation for Flows in Heterogeneous Media by :
Download or read book Multiscale Analysis and Computation for Flows in Heterogeneous Media written by and published by . This book was released on 2016 with total page 9 pages. Available in PDF, EPUB and Kindle. Book excerpt: Our work in this project is aimed at making fundamental advances in multiscale methods for flow and transport in highly heterogeneous porous media. The main thrust of this research is to develop a systematic multiscale analysis and efficient coarse-scale models that can capture global effects and extend existing multiscale approaches to problems with additional physics and uncertainties. A key emphasis is on problems without an apparent scale separation. Multiscale solution methods are currently under active investigation for the simulation of subsurface flow in heterogeneous formations. These procedures capture the effects of fine-scale permeability variations through the calculation of specialized coarse-scale basis functions. Most of the multiscale techniques presented to date employ localization approximations in the calculation of these basis functions. For some highly correlated (e.g., channelized) formations, however, global effects are important and these may need to be incorporated into the multiscale basis functions. Other challenging issues facing multiscale simulations are the extension of existing multiscale techniques to problems with additional physics, such as compressibility, capillary effects, etc. In our project, we explore the improvement of multiscale methods through the incorporation of additional (single-phase flow) information and the development of a general multiscale framework for flows in the presence of uncertainties, compressible flow and heterogeneous transport, and geomechanics. We have considered (1) adaptive local-global multiscale methods, (2) multiscale methods for the transport equation, (3) operator-based multiscale methods and solvers, (4) multiscale methods in the presence of uncertainties and applications, (5) multiscale finite element methods for high contrast porous media and their generalizations, and (6) multiscale methods for geomechanics. Below, we present a brief overview of each of these contributions.
Book Synopsis An Introduction to Reservoir Simulation Using MATLAB/GNU Octave by : Knut-Andreas Lie
Download or read book An Introduction to Reservoir Simulation Using MATLAB/GNU Octave written by Knut-Andreas Lie and published by Cambridge University Press. This book was released on 2019-08-08 with total page 677 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents numerical methods for reservoir simulation, with efficient implementation and examples using widely-used online open-source code, for researchers, professionals and advanced students. This title is also available as Open Access on Cambridge Core.
Book Synopsis Computational Mathematics, Algorithms, and Data Processing by : Daniele Mortari
Download or read book Computational Mathematics, Algorithms, and Data Processing written by Daniele Mortari and published by MDPI. This book was released on 2020-12-07 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: “Computational Mathematics, Algorithms, and Data Processing” of MDPI consists of articles on new mathematical tools and numerical methods for computational problems. Topics covered include: numerical stability, interpolation, approximation, complexity, numerical linear algebra, differential equations (ordinary, partial), optimization, integral equations, systems of nonlinear equations, compression or distillation, and active learning.
Book Synopsis Applied Hydrogeology of Fractured Rocks by : B.B.S. Singhal †
Download or read book Applied Hydrogeology of Fractured Rocks written by B.B.S. Singhal † and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hydrology is a topical and growing subject, as the earth's water resources become scarcer and more vulnerable. Although more than half the surface area of continents is covered with hard fractured rocks, there has until now been no single book available dealing specifically with fractured rock hydrogeology. This book deals comprehensively with the fundamental principles for understanding these rocks, as well as with exploration techniques and assessment. It also provides in-depth discussion of structural mapping, remote sensing, geophysical exploration, GIS, field hydraulic testing, groundwater quality and contamination, geothermal reservoirs, and resources assessment and management. Hydrogeological aspects of various lithology groups, including crystalline rocks, volcanic rocks, carbonate rocks and clastic formations, are dealt with separately, using and discussing examples from all over the world. Applied Hydrogeology of Fractured Rocks will be an invaluable reference source for postgraduate students, researchers, exploration scientists, and engineers engaged in the field of groundwater development in fractured rock areas.
Book Synopsis Computational Methods for Multiphase Flows in Porous Media by : Zhangxin Chen
Download or read book Computational Methods for Multiphase Flows in Porous Media written by Zhangxin Chen and published by SIAM. This book was released on 2006-04-01 with total page 551 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a fundamental and practical introduction to the use of computational methods. A thorough discussion of practical aspects of the subject is presented in a consistent manner, and the level of treatment is rigorous without being unnecessarily abstract. Each chapter ends with bibliographic information and exercises.
Book Synopsis Petroleum Reservoir Simulation by : K. Aziz
Download or read book Petroleum Reservoir Simulation written by K. Aziz and published by Springer. This book was released on 1979 with total page 508 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book contains a relatively complete treatment of finite-difference models of black-oil type rservoirs.
Book Synopsis Reduced Basis Methods for Partial Differential Equations by : Alfio Quarteroni
Download or read book Reduced Basis Methods for Partial Differential Equations written by Alfio Quarteroni and published by Springer. This book was released on 2015-08-19 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a basic introduction to reduced basis (RB) methods for problems involving the repeated solution of partial differential equations (PDEs) arising from engineering and applied sciences, such as PDEs depending on several parameters and PDE-constrained optimization. The book presents a general mathematical formulation of RB methods, analyzes their fundamental theoretical properties, discusses the related algorithmic and implementation aspects, and highlights their built-in algebraic and geometric structures. More specifically, the authors discuss alternative strategies for constructing accurate RB spaces using greedy algorithms and proper orthogonal decomposition techniques, investigate their approximation properties and analyze offline-online decomposition strategies aimed at the reduction of computational complexity. Furthermore, they carry out both a priori and a posteriori error analysis. The whole mathematical presentation is made more stimulating by the use of representative examples of applicative interest in the context of both linear and nonlinear PDEs. Moreover, the inclusion of many pseudocodes allows the reader to easily implement the algorithms illustrated throughout the text. The book will be ideal for upper undergraduate students and, more generally, people interested in scientific computing. All these pseudocodes are in fact implemented in a MATLAB package that is freely available at https://github.com/redbkit
Book Synopsis Principles of Multiscale Modeling by : Weinan E
Download or read book Principles of Multiscale Modeling written by Weinan E and published by Cambridge University Press. This book was released on 2011-07-07 with total page 485 pages. Available in PDF, EPUB and Kindle. Book excerpt: A systematic discussion of the fundamental principles, written by a leading contributor to the field.
Book Synopsis Flow and Transport in Fractured Porous Media by : Peter Dietrich
Download or read book Flow and Transport in Fractured Porous Media written by Peter Dietrich and published by Springer Science & Business Media. This book was released on 2005-03-02 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book addresses the characterization of flow and transport in porous fractured media from experimental and modeling perspectives. The volume explores porous media problems, from the origin of the present natural porous structures, to their characterization, and various flow and transport phenomena that exist within the porous media. Examples are miscible displacements in porous media and fractured rock and the physical and chemical interactions within porous fractured aquifers. The book is a comprehensive presentation of investigations performed and analysed on different scales, supporting the understanding and application of experimental studies and numerical simulations.
Book Synopsis Introduction to Numerical Methods for Variational Problems by : Hans Petter Langtangen
Download or read book Introduction to Numerical Methods for Variational Problems written by Hans Petter Langtangen and published by Springer Nature. This book was released on 2019-09-26 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook teaches finite element methods from a computational point of view. It focuses on how to develop flexible computer programs with Python, a programming language in which a combination of symbolic and numerical tools is used to achieve an explicit and practical derivation of finite element algorithms. The finite element library FEniCS is used throughout the book, but the content is provided in sufficient detail to ensure that students with less mathematical background or mixed programming-language experience will equally benefit. All program examples are available on the Internet.
Book Synopsis Non Fickian Solute Transport by : William Taylor
Download or read book Non Fickian Solute Transport written by William Taylor and published by . This book was released on 2015-02-12 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This research-based book provides a mathematical approach based on stochastic calculus which describes state-of-the-art information regarding porous media science and engineering - prediction of dispersivity from covariance of hydraulic conductivity (velocity). The complication is of great significance for tracer examination, for improved recovery by injection of miscible gases, etc. The book elucidates a generalized mathematical model and efficient numerical methodologies that may greatly affect the stochastic porous media hydrodynamics. It begins with a descriptive basic analysis of the complication of scale dependence of the dispersion coefficient in porous media. Furthermore, relevant topics of stochastic calculus which would be helpful in modeling are discussed subsequently. An in-depth elaborative discussion regarding the development of a generalized stochastic solute transport model for any provided velocity covariance without conferring to fickian expectations from laboratory scale to field scale is also illustrated in this book. The mathematical approaches described in this book will serve as useful solutions for several other complications associated with chemical dispersion in porous media.
Book Synopsis Flow and Transport Properties of Unconventional Reservoirs 2018 by : Jianchao Cai
Download or read book Flow and Transport Properties of Unconventional Reservoirs 2018 written by Jianchao Cai and published by MDPI. This book was released on 2019-07-23 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: Unconventional reservoirs are usually complex and highly heterogeneous, such as shale, coal, and tight sandstone reservoirs. The strong physical and chemical interactions between fluids and pore surfaces lead to the inapplicability of conventional approaches for characterizing fluid flow in these low-porosity and ultralow-permeability reservoir systems. Therefore, new theories and techniques are urgently needed to characterize petrophysical properties, fluid transport, and their relationships at multiple scales for improving production efficiency from unconventional reservoirs. This book presents fundamental innovations gathered from 21 recent works on novel applications of new techniques and theories in unconventional reservoirs, covering the fields of petrophysical characterization, hydraulic fracturing, fluid transport physics, enhanced oil recovery, and geothermal energy. Clearly, the research covered in this book is helpful to understand and master the latest techniques and theories for unconventional reservoirs, which have important practical significance for the economic and effective development of unconventional oil and gas resources.
Book Synopsis Geometric Modelling, Numerical Simulation, and Optimization: by : Geir Hasle
Download or read book Geometric Modelling, Numerical Simulation, and Optimization: written by Geir Hasle and published by Springer Science & Business Media. This book was released on 2007-06-10 with total page 559 pages. Available in PDF, EPUB and Kindle. Book excerpt: This edited volume addresses the importance of mathematics for industry and society by presenting highlights from contract research at the Department of Applied Mathematics at SINTEF, the largest independent research organization in Scandinavia. Examples range from computer-aided geometric design, via general purpose computing on graphics cards, to reservoir simulation for enhanced oil recovery. Contributions are written in a tutorial style.
