Generalized Discontinuous Multiscale Methods For Flows In Highly Heterogeneous Porous Media
DOWNLOAD
Download Generalized Discontinuous Multiscale Methods For Flows In Highly Heterogeneous Porous Media PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Generalized Discontinuous Multiscale Methods For Flows In Highly Heterogeneous Porous Media book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
Generalized Discontinuous Multiscale Methods For Flows In Highly Heterogeneous Porous Media
DOWNLOAD
Author : Minam Moon
language : en
Publisher:
Release Date : 2015
Generalized Discontinuous Multiscale Methods For Flows In Highly Heterogeneous Porous Media written by Minam Moon and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with categories.
This dissertation is devoted to the development, study and testing of numerical methods for elliptic and parabolic equations with heterogeneous coefficients. The motivation for this study is to meet the need for fast and robust methods for numerical upscaling and simulation of single and multi-phase fluid flow in highly heterogeneous porous media. We consider the multiscale model reduction technique in the framework of the discontinuous Galerkin (DG) and the hybridizable discontinuous Galerkin (HDG) finite element methods. First, we design multiscale finite element methods for second order elliptic equations by applying the symmetric interior penalty discontinuous Galekin finite element method. We propose two different types of finite element spaces on the coarse mesh within DG framework. The first type of spaces is based on a local spectral problem that uses an interior weighted L2-norm and a boundary weighted L2-norm for computing the mass matrix. The second choice is based on generation of a snapshot space and subsequent selection of a subspace of a reduced dimension. Second, we develop multiscale model reduction methods within the HDG framework. We provide construction of several multiscale finite element spaces (related to the coarse-mesh edges) that guarantee a reasonable approximation on a reduced dimensional space of the numerical traces. In these approaches, we use local snapshot spaces and local spectral decomposition following the concept of Generalized Multiscale Finite Element Methods. We also provide a general framework for systematic construction of multiscale spaces. By using local snapshots we were able to add local features to the solution space and to avoid high dimensional representation of trace spaces. Further, we extend multiscale finite element methods within HDG method to nonlinear and/or time-dependent problems. These extensions demonstrate the potential of the proposed constructions for some advanced and more practical applications. For most of the proposed methods, we investigate their stability and derive error estimates for the approximate solutions. Furthermore we study the performance of all proposed methods on a representative number of numerical examples. In the numerical tests, we use various permeability data of highly heterogeneous porous media and contrasts ranging from 103 to 106. Since the exact solution is in general unknown, we first generate solutions on a very fine mesh and use them as reference solutions in our tests. The numerical results confirm the theoretical study of the accuracy of the proposed methods and their robustness with respect to the media contrast. Our numerical experiments also show that the proposed methods could be implemented in a practical and efficient way. The electronic version of this dissertation is accessible from http://hdl.handle.net/1969.1/155430
Multiscale Methods For Flow And Transport In Heterogeneous Porous Media
DOWNLOAD
Author : Ruben Juanes
language : en
Publisher:
Release Date : 2008
Multiscale Methods For Flow And Transport In Heterogeneous Porous Media written by Ruben Juanes and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with categories.
Special Issue On Multiscale Methods For Flow And Transport In Heterogeneous Porous Media
DOWNLOAD
Author : Ruben Juanes
language : en
Publisher:
Release Date : 2008
Special Issue On Multiscale Methods For Flow And Transport In Heterogeneous Porous Media written by Ruben Juanes and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with categories.
Multiscale Model Reduction
DOWNLOAD
Author : Eric Chung
language : en
Publisher: Springer Nature
Release Date : 2023-06-07
Multiscale Model Reduction written by Eric Chung and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-06-07 with Mathematics categories.
This monograph is devoted to the study of multiscale model reduction methods from the point of view of multiscale finite element methods. Multiscale numerical methods have become popular tools for modeling processes with multiple scales. These methods allow reducing the degrees of freedom based on local offline computations. Moreover, these methods allow deriving rigorous macroscopic equations for multiscale problems without scale separation and high contrast. Multiscale methods are also used to design efficient solvers. This book offers a combination of analytical and numerical methods designed for solving multiscale problems. The book mostly focuses on methods that are based on multiscale finite element methods. Both applications and theoretical developments in this field are presented. The book is suitable for graduate students and researchers, who are interested in this topic.
Multiscale Analysis And Computation For Flows In Heterogeneous Media
DOWNLOAD
Author :
language : en
Publisher:
Release Date : 2016
Multiscale Analysis And Computation For Flows In Heterogeneous Media written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with categories.
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.
Computational Mathematics Algorithms And Data Processing
DOWNLOAD
Author : Daniele Mortari
language : en
Publisher: MDPI
Release Date : 2020-12-07
Computational Mathematics Algorithms And Data Processing written by Daniele Mortari and has been published by MDPI this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-07 with Technology & Engineering categories.
“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.
Handbook Of Geomathematics
DOWNLOAD
Author : Willi Freeden
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-08-13
Handbook Of Geomathematics written by Willi Freeden and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-08-13 with Mathematics categories.
During the last three decades geosciences and geo-engineering were influenced by two essential scenarios: First, the technological progress has changed completely the observational and measurement techniques. Modern high speed computers and satellite based techniques are entering more and more all geodisciplines. Second, there is a growing public concern about the future of our planet, its climate, its environment, and about an expected shortage of natural resources. Obviously, both aspects, viz. efficient strategies of protection against threats of a changing Earth and the exceptional situation of getting terrestrial, airborne as well as spaceborne data of better and better quality explain the strong need of new mathematical structures, tools, and methods. Mathematics concerned with geoscientific problems, i.e., Geomathematics, is becoming increasingly important. The ‘Handbook Geomathematics’ as a central reference work in this area comprises the following scientific fields: (I) observational and measurement key technologies (II) modelling of the system Earth (geosphere, cryosphere, hydrosphere, atmosphere, biosphere) (III) analytic, algebraic, and operator-theoretic methods (IV) statistical and stochastic methods (V) computational and numerical analysis methods (VI) historical background and future perspectives.
Multiscale Modeling And Simulation In Science
DOWNLOAD
Author : Björn Engquist
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-02-11
Multiscale Modeling And Simulation In Science written by Björn Engquist and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-02-11 with Computers categories.
Most problems in science involve many scales in time and space. An example is turbulent ?ow where the important large scale quantities of lift and drag of a wing depend on the behavior of the small vortices in the boundarylayer. Another example is chemical reactions with concentrations of the species varying over seconds and hours while the time scale of the oscillations of the chemical bonds is of the order of femtoseconds. A third example from structural mechanics is the stress and strain in a solid beam which is well described by macroscopic equations but at the tip of a crack modeling details on a microscale are needed. A common dif?culty with the simulation of these problems and many others in physics, chemistry and biology is that an attempt to represent all scales will lead to an enormous computational problem with unacceptably long computation times and large memory requirements. On the other hand, if the discretization at a coarse level ignoresthe?nescale informationthenthesolutionwillnotbephysicallymeaningful. The in?uence of the ?ne scales must be incorporated into the model. This volume is the result of a Summer School on Multiscale Modeling and S- ulation in Science held at Boso ¤n, Lidingo ¤ outside Stockholm, Sweden, in June 2007. Sixty PhD students from applied mathematics, the sciences and engineering parti- pated in the summer school.
Finite Difference Methods Theory And Applications
DOWNLOAD
Author : Ivan Dimov
language : en
Publisher: Springer
Release Date : 2019-01-28
Finite Difference Methods Theory And Applications written by Ivan Dimov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-28 with Computers categories.
This book constitutes the refereed conference proceedings of the 7th International Conference on Finite Difference Methods, FDM 2018, held in Lozenetz, Bulgaria, in June 2018.The 69 revised full papers presented together with 11 invited papers were carefully reviewed and selected from 94 submissions. They deal with many modern and new numerical techniques like splitting techniques, Green’s function method, multigrid methods, and immersed interface method.
Multiscale Mortar Mixed Finite Element Methods For Flow Problems In Highly Heterogeneous Porous Media
DOWNLOAD
Author : Hailong Xiao
language : en
Publisher:
Release Date : 2013
Multiscale Mortar Mixed Finite Element Methods For Flow Problems In Highly Heterogeneous Porous Media written by Hailong Xiao and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with categories.
We use Darcy's law and conservation of mass to model the flow of a fluid through a porous medium. It is a second order elliptic system with a heterogeneous coefficient. We consider the equations written in mixed form. In the heterogeneous case, we define a new multiscale mortar space that incorporates purely local information from homogenization theory to better approximate the solution along the interfaces with just a few degrees of freedom. In the case of a locally periodic heterogeneous coefficient of period epsilon, we prove that the new method achieves both optimal order error estimates in the discretization parameters and good approximation when epsilon is small. Moreover, we present numerical examples to assess its performance when the coefficient is not obviously locally periodic. We show that the new mortar method works well, and better than polynomial mortar spaces. On the other hand, we also propose to use multiscale mortars as a coarse component to construct a two-level preconditioner for the saddle point linear system arising from the fine scale discretization of the mixed finite element system. The two-level preconditioners are constructed based on the interfaces. We propose a framework to define the interpolation operators for the face based two-level preconditioners for different combination of coarse and fine scale mortar spaces for matching and nonmatching grids. In this dissertation, we show that for quasi-homogeneous problems and matching grids, the condition number of the preconditioned interface operator is bounded by (log(H/h))2, which is the same as the traditional two-level preconditioners, for quasi-homogeneous problems. We show several numerical examples to demonstrate that for the strongly heterogeneous porous media, it is often desirable and even necessary to use a higher dimensional coarse mortar space to construct the coarse preconditioner to achieve convergence. We apply our ideas to study slightly compressible single phase and two-phase flow in a porous medium. We find that for the nonlinear single phase problem, the two-level preconditioners could be successfully applied to the symmetrized linear system. For the two-phase problem, using the fine scale, instead of multiscale, velocity solutions from the flow problem can greatly benefit the transport problem.