The Discontinuous Enrichment Method (DEM) for Multi-scale Transport Problems PDF Download
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Author: Irina Kalashnikova
Publisher: Stanford University
ISBN:
Category :
Languages : en
Pages : 178
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Book Description
A discontinuous enrichment method (DEM) for the efficient finite element solution of advection-dominated transport problems in fluid mechanics whose solutions are known to possess multi-scale features is developed. Attention is focused specifically on the two-dimensional (2D) advection-diffusion equation, the usual scalar model for the Navier-Stokes equations. Following the basic DEM methodology [1], the usual Galerkin polynomial approximation is locally enriched by the free-space solutions to the governing homogeneous partial differential equation (PDE). For the constant-coefficient advection-diffusion equation, several families of free-space solutions are derived. These include a family of exponential functions that exhibit a steep gradient in some flow direction, and a family of discontinuous polynomials. A parametrization of the former class of functions with respect to an angle parameter is developed, so as to enable the systematic design and implementation of DEM elements of arbitrary orders. It is shown that the original constant-coefficient methodology has a natural extension to variable-coefficient advection-diffusion problems. For variable-coefficient transport problems, the approximation properties of DEM can be improved by augmenting locally the enrichment space with a "higher-order" enrichment function that solves the governing PDE with the advection field a(x) linearized to second order. A space of Lagrange multipliers, introduced at the element interfaces to enforce a weak continuity of the solution and related to the normal derivatives of the enrichment functions, is developed. The construction of several low and higher-order DEM elements fitting this paradigm is discussed in detail. Numerical results for several constant as well as variable-coefficient advection-diffusion benchmark problems reveal that these DEM elements outperform their standard Galerkin and stabilized Galerkin counterparts of comparable computational complexity by a large margin, especially when the flow is advection-dominated.
Author: Irina Kalashnikova
Publisher: Stanford University
ISBN:
Category :
Languages : en
Pages : 178
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Book Description
A discontinuous enrichment method (DEM) for the efficient finite element solution of advection-dominated transport problems in fluid mechanics whose solutions are known to possess multi-scale features is developed. Attention is focused specifically on the two-dimensional (2D) advection-diffusion equation, the usual scalar model for the Navier-Stokes equations. Following the basic DEM methodology [1], the usual Galerkin polynomial approximation is locally enriched by the free-space solutions to the governing homogeneous partial differential equation (PDE). For the constant-coefficient advection-diffusion equation, several families of free-space solutions are derived. These include a family of exponential functions that exhibit a steep gradient in some flow direction, and a family of discontinuous polynomials. A parametrization of the former class of functions with respect to an angle parameter is developed, so as to enable the systematic design and implementation of DEM elements of arbitrary orders. It is shown that the original constant-coefficient methodology has a natural extension to variable-coefficient advection-diffusion problems. For variable-coefficient transport problems, the approximation properties of DEM can be improved by augmenting locally the enrichment space with a "higher-order" enrichment function that solves the governing PDE with the advection field a(x) linearized to second order. A space of Lagrange multipliers, introduced at the element interfaces to enforce a weak continuity of the solution and related to the normal derivatives of the enrichment functions, is developed. The construction of several low and higher-order DEM elements fitting this paradigm is discussed in detail. Numerical results for several constant as well as variable-coefficient advection-diffusion benchmark problems reveal that these DEM elements outperform their standard Galerkin and stabilized Galerkin counterparts of comparable computational complexity by a large margin, especially when the flow is advection-dominated.
Author: Irina Kalashnikova Tezaur
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
A discontinuous enrichment method (DEM) for the efficient finite element solution of advection-dominated transport problems in fluid mechanics whose solutions are known to possess multi-scale features is developed. Attention is focused specifically on the two-dimensional (2D) advection-diffusion equation, the usual scalar model for the Navier-Stokes equations. Following the basic DEM methodology [1], the usual Galerkin polynomial approximation is locally enriched by the free-space solutions to the governing homogeneous partial differential equation (PDE). For the constant-coefficient advection-diffusion equation, several families of free-space solutions are derived. These include a family of exponential functions that exhibit a steep gradient in some flow direction, and a family of discontinuous polynomials. A parametrization of the former class of functions with respect to an angle parameter is developed, so as to enable the systematic design and implementation of DEM elements of arbitrary orders. It is shown that the original constant-coefficient methodology has a natural extension to variable-coefficient advection-diffusion problems. For variable-coefficient transport problems, the approximation properties of DEM can be improved by augmenting locally the enrichment space with a "higher-order" enrichment function that solves the governing PDE with the advection field a(x) linearized to second order. A space of Lagrange multipliers, introduced at the element interfaces to enforce a weak continuity of the solution and related to the normal derivatives of the enrichment functions, is developed. The construction of several low and higher-order DEM elements fitting this paradigm is discussed in detail. Numerical results for several constant as well as variable-coefficient advection-diffusion benchmark problems reveal that these DEM elements outperform their standard Galerkin and stabilized Galerkin counterparts of comparable computational complexity by a large margin, especially when the flow is advection-dominated.
Author: Erwin Stein
Publisher:
ISBN:
Category : Dynamics
Languages : en
Pages : 870
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Book Description
The Encyclopedia of Computational Mechanics provides a comprehensive collection of knowledge about the theory and practice of computational mechanics.
Author: Chongmin Song
Publisher: John Wiley & Sons
ISBN: 1119388457
Category : Science
Languages : en
Pages : 775
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Book Description
An informative look at the theory, computer implementation, and application of the scaled boundary finite element method This reliable resource, complete with MATLAB, is an easy-to-understand introduction to the fundamental principles of the scaled boundary finite element method. It establishes the theory of the scaled boundary finite element method systematically as a general numerical procedure, providing the reader with a sound knowledge to expand the applications of this method to a broader scope. The book also presents the applications of the scaled boundary finite element to illustrate its salient features and potentials. The Scaled Boundary Finite Element Method: Introduction to Theory and Implementation covers the static and dynamic stress analysis of solids in two and three dimensions. The relevant concepts, theory and modelling issues of the scaled boundary finite element method are discussed and the unique features of the method are highlighted. The applications in computational fracture mechanics are detailed with numerical examples. A unified mesh generation procedure based on quadtree/octree algorithm is described. It also presents examples of fully automatic stress analysis of geometric models in NURBS, STL and digital images. Written in lucid and easy to understand language by the co-inventor of the scaled boundary element method Provides MATLAB as an integral part of the book with the code cross-referenced in the text and the use of the code illustrated by examples Presents new developments in the scaled boundary finite element method with illustrative examples so that readers can appreciate the significant features and potentials of this novel method—especially in emerging technologies such as 3D printing, virtual reality, and digital image-based analysis The Scaled Boundary Finite Element Method: Introduction to Theory and Implementation is an ideal book for researchers, software developers, numerical analysts, and postgraduate students in many fields of engineering and science.
Author: Peter Wriggers
Publisher: Springer Science & Business Media
ISBN: 3211772987
Category : Science
Languages : en
Pages : 252
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Book Description
Topics of this book span the range from spatial and temporal discretization techniques for contact and impact problems with small and finite deformations over investigations on the reliability of micromechanical contact models over emerging techniques for rolling contact mechanics to homogenization methods and multi-scale approaches in contact problems.
Author: Dimitri Gidaspow
Publisher: Elsevier
ISBN: 0080512267
Category : Science
Languages : en
Pages : 489
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Book Description
Useful as a reference for engineers in industry and as an advanced level text for graduate engineering students, Multiphase Flow and Fluidization takes the reader beyond the theoretical to demonstrate how multiphase flow equations can be used to provide applied, practical, predictive solutions to industrial fluidization problems. Written to help advance progress in the emerging science of multiphase flow, this book begins with the development of the conservation laws and moves on through kinetic theory, clarifying many physical concepts (such as particulate viscosity and solids pressure) and introducing the new dependent variable--the volume fraction of the dispersed phase. Exercises at the end of each chapterare provided for further study and lead into applications not covered in the text itself. Treats fluidization as a branch of transport phenomena Demonstrates how to do transient, multidimensional simulation of multiphase processes The first book to apply kinetic theory to flow of particulates Is the only book to discuss numerical stability of multiphase equations and whether or not such equations are well-posed Explains the origin of bubbles and the concept of critical granular flow Presents clearly written exercises at the end of each chapter to facilitate understanding and further study
Author: Amir Faghri
Publisher: Academic Press
ISBN:
Category : Multiphase flow
Languages : en
Pages : 1072
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Book Description
Engineering students in a wide variety of engineering disciplines from mechanical and chemical to biomedical and materials engineering must master the principles of transport phenomena as an essential tool in analyzing and designing any system or systems wherein momentum, heat and mass are transferred. This textbook was developed to address that need, with a clear presentation of the fundamentals, ample problem sets to reinforce that knowledge, and tangible examples of how this knowledge is put to use in engineering design. Professional engineers, too, will find this book invaluable as reference for everything from heat exchanger design to chemical processing system design and more. * Develops an understanding of the thermal and physical behavior of multiphase systems with phase change, including microscale and porosity, for practical applications in heat transfer, bioengineering, materials science, nuclear engineering, environmental engineering, process engineering, biotechnology and nanotechnology * Brings all three forms of phase change, i.e., liquid vapor, solid liquid and solid vapor, into one volume and describes them from one perspective in the context of fundamental treatment * Presents the generalized integral and differential transport phenomena equations for multi-component multiphase systems in local instance as well as averaging formulations. The molecular approach is also discussed with the connection between microscopic and molecular approaches * Presents basic principles of analyzing transport phenomena in multiphase systems with emphasis on melting, solidification, sublimation, vapor deposition, condensation, evaporation, boiling and two-phase flow heat transfer at the micro and macro levels * Solid/liquid/vapor interfacial phenomena, including the concepts of surface tension, wetting phenomena, disjoining pressure, contact angle, thin films and capillary phenomena, including interfacial balances for mass, species, momentum, and energy for multi-component and multiphase interfaces are discussed * Ample examples and end-of-chapter problems, with Solutions Manual and PowerPoint presentation available to the instructors
Author: Amir R. Khoei
Publisher: John Wiley & Sons
ISBN: 1118457684
Category : Science
Languages : en
Pages : 600
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Book Description
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
Author: Timon Rabczuk
Publisher: MDPI
ISBN: 3039216864
Category : Technology & Engineering
Languages : en
Pages : 406
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Book Description
This book offers a collection of 17 scientific papers about the computational modeling of fracture. Some of the manuscripts propose new computational methods and/or how to improve existing cutting edge methods for fracture. These contributions can be classified into two categories: 1. Methods which treat the crack as strong discontinuity such as peridynamics, scaled boundary elements or specific versions of the smoothed finite element methods applied to fracture and 2. Continuous approaches to fracture based on, for instance, phase field models or continuum damage mechanics. On the other hand, the book also offers a wide range of applications where state-of-the-art techniques are employed to solve challenging engineering problems such as fractures in rock, glass, concrete. Also, larger systems such as fracture in subway stations due to fire, arch dams, or concrete decks are studied.
Author: John Dewey
Publisher: Createspace Independent Publishing Platform
ISBN:
Category : Juvenile Nonfiction
Languages : en
Pages : 456
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Book Description
. Renewal of Life by Transmission. The most notable distinction between living and inanimate things is that the former maintain themselves by renewal. A stone when struck resists. If its resistance is greater than the force of the blow struck, it remains outwardly unchanged. Otherwise, it is shattered into smaller bits. Never does the stone attempt to react in such a way that it may maintain itself against the blow, much less so as to render the blow a contributing factor to its own continued action. While the living thing may easily be crushed by superior force, it none the less tries to turn the energies which act upon it into means of its own further existence. If it cannot do so, it does not just split into smaller pieces (at least in the higher forms of life), but loses its identity as a living thing. As long as it endures, it struggles to use surrounding energies in its own behalf. It uses light, air, moisture, and the material of soil. To say that it uses them is to say that it turns them into means of its own conservation. As long as it is growing, the energy it expends in thus turning the environment to account is more than compensated for by the return it gets: it grows. Understanding the word "control" in this sense, it may be said that a living being is one that subjugates and controls for its own continued activity the energies that would otherwise use it up. Life is a self-renewing process through action upon the environment.
