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Algebraic Multiscale Solver For Flow Problems In Heterogeneous Porous Media
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Book Synopsis Algebraic Multiscale Solver for Flow Problems in Heterogeneous Porous Media by : Yixuan Wang
Download or read book Algebraic Multiscale Solver for Flow Problems in Heterogeneous Porous Media written by Yixuan Wang and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical simulations of multiphase flow in porous media lead to linear systems which are very large and fall beyond the scope of classical iterative solvers. This has motivated extensive research on the development of solution techniques for such systems, including multiscale methods to reduce the computational complexity. The objective of this dissertation is to develop an efficient and scalable linear solution strategy based on multiscale methods for flow problems (pressure equations) arising from reservoir simulation. This work consists of three parts. First, an Algebraic Multiscale Solver (AMS) framework for incompressible flow problems is described. Second, a monotone Multiscale Finite Volume method is proposed to achieve a physical and mass conservative pressure solution. Finally, AMS is extended to simulate flow in heterogeneous reservoirs with complex well configurations.
Book Synopsis Algebraic Multiscale Finite-volume Methods for Reservoir Simulation by : Zhou Hui
Download or read book Algebraic Multiscale Finite-volume Methods for Reservoir Simulation written by Zhou Hui and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the major challenges in reservoir simulation is posed by the existence of multiple scales in reservoirs and the resulting high resolution geophysical models. It is usually too expensive to compute directly on the finest geo-cellular scale. On the other hand, the accuracy of simulating subsurface flow relies strongly on the detailed geophysical properties of natural heterogeneous formations. Multiscale methods have been shown to be very promising to bridge the gap between the geological and flow-simulation scales. However, there are a few limitations in existing multiscale methods, e.g., the extension to physical mechanisms (such as compressibility, gravity and capillary pressure), and difficulties for cases with channelized permeability or high anisotropy. Moreover, the multiscale method has been applied only to the flow problem for efficient solutions of the pressure and velocity fields, while the transport problem is solved on the fine scale. In this work, we develop an algebraic multiscale framework for coupled flow and transport problems in heterogeneous porous media. An operator-based multiscale method (OBMM) is proposed to solve general multiphase flow problems. The key ingredients of the method are two algebraic multiscale operators, prolongation and restriction, with which the multiscale solution can be constructed algebraically. It is straightforward to extend OBMM to general flow problems that involve more physical mechanisms, such as compressibility, gravity and capillary pressure. The efficiency and accuracy of OBMM are demonstrated by a wide range of problems. An adaptive multiscale formulation for the saturation equations is developed within the algebraic multiscale framework, which is the first multiscale treatment of transport problems. Our multiscale formulation employs a conservative restriction operator and three adaptive prolongation operators. For the time interval of interest, the physical domain is divided into three distinct regions according to the coarse-scale saturation solution. Then, different prolongation operators are defined and used adaptively in different regions to construct the fine-scale saturation field. The multiscale computations of coupled flow and transport further improve the computational efficiency over the original multiscale finite-volume method, which is already significantly more efficient than fine-scale methods. An efficient two-stage algebraic multiscale (TAMS) method is also developed, which overcomes the limitations of the multiscale finite-volume method for channelized permeability fields and highly anisotropic problems. The TAMS method consists of two stages, one global and one local. In the global stage, a multiscale solution is obtained purely algebraically from the fine-scale matrix. The prolongation operator is obtained algebraically using the wirebasket ordered reduced system of the original fine-scale coefficient matrix. In the second stage, a local solution is constructed from a simple block preconditioner, such as Block ILU(0) (BILU), or an Additive Schwarz (AS) method. The TAMS method is purely algebraic and only needs the fine-scale coefficient matrix and the wirebasket ordering information of the multiscale grid. Thus, the TAMS method can be applied as a preconditioner for solving the large-scale linear systems associated with the flow problem. The TAMS method converges rapidly even for problems with channelized permeability fields and high anisotropy ratios. TAMS also preserve the favorable property of local mass conservation of the multiscale finite-volume method. Therefore, the TAMS method can be applied as either an efficient linear solver or a fast approximation approach with very good accuracy.
Book Synopsis Supercomputing by : Vladimir Voevodin
Download or read book Supercomputing written by Vladimir Voevodin and published by Springer Nature. This book was released on 2022-12-15 with total page 713 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 8th Russian Supercomputing Days on Supercomputing, RuSCDays 2022, which took place in Moscow, Russia, in September 2022. The 49 full papers and 1 short paper presented in this volume were carefully reviewed and selected from 94 submissions. The papers are organized in the following topical sections: Supercomputer Simulation; HPC, BigData, AI: Architectures, Technologies, Tools; Distributed and Cloud Computing.
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 Computational Science – ICCS 2023 by : Jiří Mikyška
Download or read book Computational Science – ICCS 2023 written by Jiří Mikyška and published by Springer Nature. This book was released on 2023-06-28 with total page 809 pages. Available in PDF, EPUB and Kindle. Book excerpt: The five-volume set LNCS 14073-14077 constitutes the proceedings of the 23rd International Conference on Computational Science, ICCS 2023, held in Prague, Czech Republic, during July 3-5, 2023. The total of 188 full papers and 94 short papers presented in this book set were carefully reviewed and selected from 530 submissions. 54 full and 37 short papers were accepted to the main track; 134 full and 57 short papers were accepted to the workshops/thematic tracks. The theme for 2023, "Computation at the Cutting Edge of Science", highlights the role of Computational Science in assisting multidisciplinary research. This conference was a unique event focusing on recent developments in scalable scientific algorithms, advanced software tools; computational grids; advanced numerical methods; and novel application areas. These innovative novel models, algorithms, and tools drive new science through efficient application in physical systems, computational and systems biology, environmental systems, finance, and others.
Book Synopsis Generalized Discontinuous Multiscale Methods for Flows in Highly Heterogeneous Porous Media by : Minam Moon
Download or read book Generalized Discontinuous Multiscale Methods for Flows in Highly Heterogeneous Porous Media written by Minam Moon and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
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 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 The Mathematics of Reservoir Simulation by : Richard E. Ewing
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 Multiscale Methods written by Jacob Fish and published by Oxford University Press. This book was released on 2010 with total page 631 pages. Available in PDF, EPUB and Kindle. Book excerpt: Small scale features and processes occurring at nanometer and femtosecond scales have a profound impact on what happens at a larger scale and over an extensive period of time. The primary objective of this volume is to reflect the state-of-the-art in multiscale mathematics, modeling, and simulations and to address the following barriers: What is the information that needs to be transferred from one model or scale to another and what physical principles must be satisfied during thetransfer of information? What are the optimal ways to achieve such transfer of information? How can variability of physical parameters at multiple scales be quantified and how can it be accounted for to ensure design robustness?The multiscale approaches in space and time presented in this volume are grouped into two main categories: information-passing and concurrent. In the concurrent approaches various scales are simultaneously resolved, whereas in the information-passing methods the fine scale is modeled and its gross response is infused into the continuum scale. The issue of reliability of multiscale modeling and simulation tools which focus on a hierarchy of multiscale models and an a posteriori model of errorestimation including uncertainty quantification, is discussed in several chapters. Component software that can be effectively combined to address a wide range of multiscale simulations is also described. Applications range from advanced materials to nanoelectromechanical systems (NEMS), biologicalsystems, and nanoporous catalysts where physical phenomena operates across 12 orders of magnitude in time scales and 10 orders of magnitude in spatial scales.This volume is a valuable reference book for scientists, engineers and graduate students practicing in traditional engineering and science disciplines as well as in emerging fields of nanotechnology, biotechnology, microelectronics and energy.
Book Synopsis The Multiscale Perturbation Method for Two-phase Flows in Porous Media by : Het Mankad
Download or read book The Multiscale Perturbation Method for Two-phase Flows in Porous Media written by Het Mankad and published by . This book was released on 2020 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation is focused on creating new multiscale mixed methods that can help reduce the computational cost and improve the accuracy of the numerical solution to the two-phase, immiscible, incompressible flow problem obtained by the operator splitting technique. The two-phase flow governing systems of equations consists of two partial differential equations:(i) a second order elliptic equation or a Poisson equation, (ii) a hyperbolic conservation law. Typically in an operator splitting technique the elliptic and the hyperbolic equations are solved sequentially. The procedure to solve the elliptic equation numerically is computationally very expensive once the size of the linear system to be solved is large. Considering that, this dissertation focuses on the development of fast and efficient solvers which are naturally parallelizable to compute the solution of the second order elliptic equation that is approximated numerically. At first, the Multiscale Perturbation Method for second order elliptic equations (MPM) is presented . This method is based on the Multiscale Mixed Method (MuMM). The MuMM, like most multiscale methods solves the elliptic equation numerically by first computing a set of local multiscale mixed basis functions (MMBFs) with special boundary condition (Robin in this case) and then solves the global problem. The MPM proposes a new algorithm that can reuse the MMBFs computed at an initial time as well as take advantage of a good initial guess by using classical perturbation techniques. Secondly, the MPM is then incorporated into the operator splitting algorithm to create a new modified algorithm (MPM-2P:Multiscale Perturbation Method for two-phase flows) that solves the two-phase flow equations numerically. A relative cost reduction which is the gain in terms of the computational time is computed between the solution obtained via the new MPM-2P and by using simply the MuMM. The results show an exceptional speed up - a reduction in computational cost from 60.8% to 96.7% - for the elliptic equation of realistic reservoir flow problems indicating that a large number of MuMM solutions in a traditional operator splitting method can be easily replaced by the inexpensive MPM-2P solutions. This makes it the most important contribution of this dissertation. Finally, a new multiscale mixed method with overlapping domain decomposition (O-MuMM) is formulated and a parallel algorithm that implements the O-MuMM computationally is proposed. Numerical results for all three methods are discussed and analyzed to prove the validity of the new methods proposed.
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 Extended Finite Element Method by : Amir R. Khoei
Download or read book Extended Finite Element Method written by Amir R. Khoei and published by John Wiley & Sons. This book was released on 2015-02-23 with total page 600 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduces the theory and applications of the extended finite element method (XFEM) in the linear and nonlinear problems of continua, structures and geomechanics Explores the concept of partition of unity, various enrichment functions, and fundamentals of XFEM formulation. Covers numerous applications of XFEM including fracture mechanics, large deformation, plasticity, multiphase flow, hydraulic fracturing and contact problems Accompanied by a website hosting source code and examples
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 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 Algorithms and Discretization Schemes for Efficient Simulation of Multiphase Flow and Transport in Porous Media by : Sebastian Benjamin Meije Bosma
Download or read book Algorithms and Discretization Schemes for Efficient Simulation of Multiphase Flow and Transport in Porous Media written by Sebastian Benjamin Meije Bosma and published by . This book was released on 2021 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Multiphase flow and transport in porous media are described by highly nonlinear partial differential equations. Implicit finite volume discretizations -- used to numerically simulate these processes -- introduce additional strong nonlinearities that make the coupled algebraic system of equations challenging to solve efficiently. When both a gas and liquid phase are present, the discrete problem is particularly difficult due to greatly contrasting fluid properties, large buoyancy forces and sizeable capillary forces. Hence, standard simulation techniques frequently fail to meet the efficiency and accuracy requirements for processes such as geologic carbon sequestration and natural gas production. As these industries grow, the need for multiphase flow and transport simulators that meet their demanding requirements intensifies. In response, this dissertation presents several strategies to reduce the computational cost of simulation. The first chapters focus on a discretization scheme that allows the nonlinear solver (Newton-Raphson) to solve the governing system of flow and transport equations more efficiently and robustly. Discontinuities in the derivative of the problem's solution space can lead to slow convergence of Newton method's linearized updates. To avoid such complications, Chapter 2 proposes a smooth total velocity hybrid upwinding scheme with weighted averaging. First, we extend the favorable transport (sub-)problem properties of hybrid upwinding to problems with three or more phases. Then, by applying phase-by-phase weighted averaging to the mobilities determining the total velocity, the scheme yields a flow subproblem that is smooth with respect to changes in the sign of phase fluxes (common in counter-current flow regimes), and is well-behaved when phase velocities are large or when co-current viscous forces dominate. On a series of challenging test cases with realistic fluids, the proposed scheme consistently outperforms existing schemes, yielding benefits from 5% to over 50% reduction in nonlinear iterations. Additionally, Chapter 2 presents a second version of the scheme using a total mass formulation that shows promising results. Overall, based on the current results, we recommend the adoption of the proposed total velocity hybrid upwinding scheme with weighting averaging as it is highly efficient and robust. Chapter 3 investigates strategies to further improve hybrid upwinding by removing the strong nonlinearity induced by the method. Specifically, a discontinuity in the flux derivative occurs in the treatment of the viscous term when the total velocity changes sign. To design a novel method, criteria for a consistent, smooth and monotone scheme are stipulated. We conclude that the requirements have conflicts and thus such a scheme is not possible. We additionally support this conclusion visually by mapping the regions of the flux function that satisfy the monotonicity requirements. A different approach to improve efficiency and accuracy of multiphase flow simulations is investigated in Chapter 4; we aim to achieve higher accuracy on coarse grids for domains with spatially heterogeneous constitutive relationships. An efficient and robust strategy for multiphase discrete interface conditions is proposed. By using phase capillary pressures as the primary variable of the local problem that computes the flux, the novel method overcomes previous limitations and extends naturally to three or more phases. This also allows us to investigate a three-phase problem's solution space with capillary boundaries (entry- and maximum-pressures) for the first time. We show how different flow regimes are delineated by the heterogeneous capillary constitutive relationships. Finally, to ensure that the local problem can be solved for complicated fluid properties, we propose a robust update damping strategy for the local nonlinear solver. The last chapter proposes an efficient preconditioner for non-M matrices that frequently arise in geomechanical problems or multipoint flow stencils. Specifically, we enhance the widely implemented multiscale restriction-smoothed basis function method with a filtering strategy. Through applications to porous media flow and linear elastic geomechanics, the method is proven to be effective for scalar and vector problems with multipoint finite volume and finite element discretization schemes, respectively.
Book Synopsis The Finite Volume Method in Computational Fluid Dynamics by : F. Moukalled
Download or read book The Finite Volume Method in Computational Fluid Dynamics written by F. Moukalled and published by Springer. This book was released on 2015-08-13 with total page 799 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook explores both the theoretical foundation of the Finite Volume Method (FVM) and its applications in Computational Fluid Dynamics (CFD). Readers will discover a thorough explanation of the FVM numerics and algorithms used for the simulation of incompressible and compressible fluid flows, along with a detailed examination of the components needed for the development of a collocated unstructured pressure-based CFD solver. Two particular CFD codes are explored. The first is uFVM, a three-dimensional unstructured pressure-based finite volume academic CFD code, implemented within Matlab. The second is OpenFOAM®, an open source framework used in the development of a range of CFD programs for the simulation of industrial scale flow problems. With over 220 figures, numerous examples and more than one hundred exercise on FVM numerics, programming, and applications, this textbook is suitable for use in an introductory course on the FVM, in an advanced course on numerics, and as a reference for CFD programmers and researchers.
