Download or read book Discontinuous Galerkin Methods for Two phase Flow in Porous Media written by Béatrice Rivière and published by . This book was released on 2004 with total page 31 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Discontinuous Galerkin Methods for Two phase Flows in Porous Media written by Christoph Grüninger and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Discontinuous Galerkin Methods for Solving Elliptic and Parabolic Equations written by Beatrice Riviere and published by SIAM. This book was released on 2008-12-18 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt: Focuses on three primal DG methods, covering both theory and computation, and providing the basic tools for analysis.

Download or read book Fundamentals of Numerical Reservoir Simulation written by D.W. Peaceman and published by Elsevier. This book was released on 2000-04-01 with total page 191 pages. Available in PDF, EPUB and Kindle. Book excerpt: The use of numerical reservoir simulation with high-speed electronic computers has gained wide acceptance throughout the petroleum industry for making engineering studies of a wide variety of oil and gas reservoirs throughout the world. These reservoir simulators have been designed for use by reservoir engineers who possess little or no background in the numerical mathematics upon which they are based. In spite of the efforts to improve numerical methods to make reservoir simulators as reliable, efficient, and automatic as possible, the user of a simulator is faced with a myriad of decisions that have nothing to do with the problem to be solved. This book combines a review of some basic reservoir mechanics with the derivation of the differential equations that reservoir simulators are designed to solve.

Download or read book Adaptive Higher Order Discontinuous Galerkin Methods for Porous media Multi phase Flow with Strong Heterogeneities written by Birane Kane and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

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.

Download or read book Part II discontinuous galerkin method applied to a single phase flow in porous media written by Beatrice Riviere and published by . This book was released on 1999 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

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.

Download or read book The Mathematics of Reservoir Simulation written by Richard E. Ewing and published by SIAM. This book was released on 2014-12-01 with total page 195 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes the state of the art of the mathematical theory and numerical analysis of imaging. Some of the applications covered in the book include computerized tomography, magnetic resonance imaging, emission tomography, electron microscopy, ultrasound transmission tomography, industrial tomography, seismic tomography, impedance tomography, and NIR imaging.

Download or read book High order Hybridizable Discontinuous Galerkin Formulation and Implicit Runge Kutta Schemes for Multiphase Flow Through Porous Media written by Albert Costa Solé and published by . This book was released on 2020 with total page 125 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation presents high-order hybridisable discontinuous Galerkin (HDG) formulations coupled with implicit Runge-Kutta (RK) methods for the simulation of one-phase flow and two-phase flow problems.High-order-methods can reduce the computational cost while obtaining more accurate solutions with less dissipation and dispersion errors than low order methods. HDG is an unstructured, high-order accurate, and stable method. The stability is imposed using a single parameter. In addition, it is a conservative method at the element level, which is an important feature when solving PDEs in a conservative form. Moreover, a hybridization procedure can be applied to reduce the size of the global linear system. To keep the stability and accuracy advantages in transient problems, we couple the HDG method with high-order implicit RK schemes.The first contribution is a stable high-order HDG formulation coupled with DIRK schemes for slightly compressible one-phase flow problem. We obtain an analytical expression for the stabilization parameter using the Engquist-Osher monotone flux scheme. The selection of the stabilization parameter is crucial to ensure the stability and to obtain the high-order properties of the method. We introduce the stabilization parameter in the Newton's solver since we analytically compute its derivatives.The second contribution is a high-order HDG formulation coupled with DIRK schemes for immiscible and incompressible two-phase flow problem. We set the water pressure and oil saturation as the main unknowns, which leads to a coupled system of two non-linear PDEs. To solve the resulting non-linear problem, we use a fix-point iterative method that alternatively solves the saturation and the pressure unknowns implicitly at each RK stage until convergence is achieved. The proposed fix-point method is memory-efficient because the saturation and the pressure are not solved at the same time.The third contribution is a discretization scheme for the two-phase flow problem with the same spatial and temporal order of convergence. High-order spatial discretization combined with low-order temporal discretizations may lead to arbitrary small time steps to obtain a low enough temporal error. Moreover, high-order stable DIRK schemes need a high number of stages above fourth-order. Thus, the computational cost can be severely hampered because a non-linear problem has to be solved at each RK stage. Thus, we couple the HDG formulation with high-order fully implicit RK schemes. These schemes can be unconditionally stable and achieve high-order temporal accuracy with few stages. Therefore, arbitrary large time steps can be used without hampering the temporal accuracy. We rewrite the non-linear system to reduce the memory footprint. Thus, we achieve a better sparsity pattern of the Jacobian matrix and less coupling between stages. Furthermore, we have adapted the previous fix-point iterative method. We first compute the saturation at all the stages by solving a single non-linear system using the Newton-Raphson method. Next, we solve the pressure equation sequentially at each RK stage, since it does not couple the unknowns at different stages.The last contribution is an efficient shock-capturing method for the immiscible and incompressible two-phase flow problem to reduce the spurious oscillations that may appear in the high-order approximations of the saturation. We introduce local artificial viscosity only in the saturation equation since only the saturation variable is non-smooth. To this end, we propose a shock sensor computed from the saturation and the post-processed saturation of the HDG method. This shock sensor is computationally efficient since the post-processed saturation is computed in an element-wise manner. Our methodology allows tracking the sharp fronts as they evolve since the shock sensor is computed at all RK stages.

Download or read book Fluid Flow and Transport in Porous Media Mathematical and Numerical Treatment written by Zhangxin Chen and published by American Mathematical Soc.. This book was released on 2002 with total page 538 pages. Available in PDF, EPUB and Kindle. Book excerpt: The June 2001 conference brought together mathematicians, computational scientists, and engineers working on the mathematical and numerical treatment of fluid flow and transport in porous media. This collection of 43 papers from that conference reports on recent advances in network flow modeling, parallel computation, optimization, upscaling, uncertainty reduction, media characterization, and chemically reactive phenomena. Topics include modeling horizontal wells using hybrid grids in reservoir simulation, a high order Lagrangian scheme for flow through unsaturated porous media, and a streamline front tracking method for two- and three- phase flow. No index. Annotation copyrighted by Book News, Inc., Portland, OR.

Download or read book Finite Volumes for Complex Applications VIII Hyperbolic Elliptic and Parabolic Problems written by Clément Cancès and published by . This book was released on 2017 with total page 559 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Fractured Porous Media written by Pierre M. Adler and published by Oxford University Press, USA. This book was released on 2013 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Advances in the Mathematical Sciences written by Alyson Deines and published by Springer. This book was released on 2018-10-31 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: Featuring research from the 2017 research symposium of the Association for Women in Mathematics, this volume presents recent findings in pure mathematics and a range of advances and novel applications in fields such as engineering, biology, and medicine. Featured topics include geometric group theory, generalized iterated wreath products of cyclic groups and symmetric groups, Conway-Coxeter friezes and mutation, and classroom experiments in teaching collegiate mathematics. A review of DNA topology and a computational study of learning-induced sequence reactivation during sharp-wave ripples are also included in this volume. Numerous illustrations and tables convey key results throughout the book. This volume highlights research from women working in academia, industry, and government. It is a helpful resource for researchers and graduate students interested in an overview of the latest research in mathematics.

Download or read book Energy Consistent Discontinuous Galerkin Methods for a Quasi incompressible Diffuse Two Phase Flow Model written by Jan Giesselmann and published by . This book was released on 2013 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Discontinuous Galerkin Methods written by Bernardo Cockburn and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: A class of finite element methods, the Discontinuous Galerkin Methods (DGM), has been under rapid development recently and has found its use very quickly in such diverse applications as aeroacoustics, semi-conductor device simula tion, turbomachinery, turbulent flows, materials processing, MHD and plasma simulations, and image processing. While there has been a lot of interest from mathematicians, physicists and engineers in DGM, only scattered information is available and there has been no prior effort in organizing and publishing the existing volume of knowledge on this subject. In May 24-26, 1999 we organized in Newport (Rhode Island, USA), the first international symposium on DGM with equal emphasis on the theory, numerical implementation, and applications. Eighteen invited speakers, lead ers in the field, and thirty-two contributors presented various aspects and addressed open issues on DGM. In this volume we include forty-nine papers presented in the Symposium as well as a survey paper written by the organiz ers. All papers were peer-reviewed. A summary of these papers is included in the survey paper, which also provides a historical perspective of the evolution of DGM and its relation to other numerical methods. We hope this volume will become a major reference in this topic. It is intended for students and researchers who work in theory and application of numerical solution of convection dominated partial differential equations. The papers were written with the assumption that the reader has some knowledge of classical finite elements and finite volume methods.

Download or read book The Gradient Discretisation Method written by Jérôme Droniou and published by Springer. This book was released on 2018-07-31 with total page 501 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents the Gradient Discretisation Method (GDM), which is a unified convergence analysis framework for numerical methods for elliptic and parabolic partial differential equations. The results obtained by the GDM cover both stationary and transient models; error estimates are provided for linear (and some non-linear) equations, and convergence is established for a wide range of fully non-linear models (e.g. Leray–Lions equations and degenerate parabolic equations such as the Stefan or Richards models). The GDM applies to a diverse range of methods, both classical (conforming, non-conforming, mixed finite elements, discontinuous Galerkin) and modern (mimetic finite differences, hybrid and mixed finite volume, MPFA-O finite volume), some of which can be built on very general meshes.span style="" ms="" mincho";mso-bidi-font-family:="" the="" core="" properties="" and="" analytical="" tools="" required="" to="" work="" within="" gdm="" are="" stressed,="" it="" is="" shown="" that="" scheme="" convergence="" can="" often="" be="" established="" by="" verifying="" a="" small="" number="" of="" properties.="" scope="" some="" featured="" techniques="" results,="" such="" as="" time-space="" compactness="" theorems="" (discrete="" aubin–simon,="" discontinuous="" ascoli–arzela),="" goes="" beyond="" gdm,="" making="" them="" potentially="" applicable="" numerical="" schemes="" not="" (yet)="" known="" fit="" into="" this="" framework.span style="font-family:" ms="" mincho";mso-bidi-font-family:="" this="" monograph="" is="" intended="" for="" graduate="" students,="" researchers="" and="" experts="" in="" the="" field="" of="" numerical="" analysis="" partial="" differential="" equations./ppiiiiibr/i/i/i/i/i/p