Spectral/hp Element Methods for CFD

Author: George Karniadakis,Spencer J. Sherwin
Publisher: Oxford University Press on Demand
ISBN: 0195102266
Category: Mathematics
Page: 390
View: 2653

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This book is an essential reference for anyone interested in the use of spectral/hp element methods in fluid dynamics. It provides a comprehensive introduction to the field together with detailed examples of the methods to the incompressible and compressible Navier-Stokes equations.

Spectral/hp Element Methods for Computational Fluid Dynamics

Second Edition
Author: George Karniadakis,Spencer J. Sherwin
Publisher: Oxford University Press on Demand
ISBN: 0198528698
Category: Mathematics
Page: 657
View: 6036

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Completely revised and expanded new edition covering the recent and significant progress in multi-domain spectral methods at both the fundamental and application level. Including new material on discontinuous Galerkin methods, non-tensorial nodal spectral element methods in simplex domains, and stabilisation and filtering techniques; this text, written by leading experts, is a must-have for students, academics and practitioners in computational fluid mechanics, applied and numerical mathematics, computational mechanics, aerospace and mechanical engineering and climate/ocean modelling.

Computer Algebra in Scientific Computing

17th International Workshop, CASC 2015, Aachen, Germany, September 14-18, 2015, Proceedings
Author: Vladimir P. Gerdt,Wolfram Koepf,Werner M. Seiler,Evgenii V. Vorozhtsov
Publisher: Springer
ISBN: 3319240218
Category: Computers
Page: 494
View: 3292

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This book constitutes the proceedings of the 17th International Workshop on Computer Algebra in Scientific Computing, CASC 2015, held in Aachen, Germany, in September 2015. The 35 full papers presented in this volume were carefully reviewed and selected from 42 submissions. They deal with the ongoing progress both in theoretical computer algebra and its expanding applications. New and closer interactions are fostered by combining the area of computer algebra methods and systems and the application of the tools of computer algebra for the solution of problems in scientific computing.

Theory and Practice of Finite Elements

Author: Alexandre Ern,Jean-Luc Guermond
Publisher: Springer Science & Business Media
ISBN: 1475743556
Category: Mathematics
Page: 526
View: 4104

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This text presenting the mathematical theory of finite elements is organized into three main sections. The first part develops the theoretical basis for the finite element methods, emphasizing inf-sup conditions over the more conventional Lax-Milgrim paradigm. The second and third parts address various applications and practical implementations of the method, respectively. It contains numerous examples and exercises.

Parallel Scientific Computing in C++ and MPI

A Seamless Approach to Parallel Algorithms and their Implementation
Author: George Em Karniadakis,Robert M. Kirby II
Publisher: Cambridge University Press
ISBN: 110749477X
Category: Computers
Page: 628
View: 6506

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Numerical algorithms, modern programming techniques, and parallel computing are often taught serially across different courses and different textbooks. The need to integrate concepts and tools usually comes only in employment or in research - after the courses are concluded - forcing the student to synthesise what is perceived to be three independent subfields into one. This book provides a seamless approach to stimulate the student simultaneously through the eyes of multiple disciplines, leading to enhanced understanding of scientific computing as a whole. The book includes both basic as well as advanced topics and places equal emphasis on the discretization of partial differential equations and on solvers. Some of the advanced topics include wavelets, high-order methods, non-symmetric systems, and parallelization of sparse systems. The material covered is suited to students from engineering, computer science, physics and mathematics.

High-Order Methods for Computational Physics

Author: Timothy J Barth,Herman Deconinck
Publisher: Springer Science & Business Media
ISBN: 366203882X
Category: Mathematics
Page: 587
View: 7692

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The development of high-order accurate numerical discretization techniques for irregular domains and meshes is often cited as one of the remaining chal lenges facing the field of computational fluid dynamics. In structural me chanics, the advantages of high-order finite element approximation are widely recognized. This is especially true when high-order element approximation is combined with element refinement (h-p refinement). In computational fluid dynamics, high-order discretization methods are infrequently used in the com putation of compressible fluid flow. The hyperbolic nature of the governing equations and the presence of solution discontinuities makes high-order ac curacy difficult to achieve. Consequently, second-order accurate methods are still predominately used in industrial applications even though evidence sug gests that high-order methods may offer a way to significantly improve the resolution and accuracy for these calculations. To address this important topic, a special course was jointly organized by the Applied Vehicle Technology Panel of NATO's Research and Technology Organization (RTO), the von Karman Institute for Fluid Dynamics, and the Numerical Aerospace Simulation Division at the NASA Ames Research Cen ter. The NATO RTO sponsored course entitled "Higher Order Discretization Methods in Computational Fluid Dynamics" was held September 14-18,1998 at the von Karman Institute for Fluid Dynamics in Belgium and September 21-25,1998 at the NASA Ames Research Center in the United States.

Parallel Computational Fluid Dynamics 2004

Multidisciplinary Applications
Author: Gabriel Winter,Jacques Periaux,Pat Fox,A. Ecer,N. Satofuka
Publisher: Elsevier
ISBN: 9780080460963
Category: Technology & Engineering
Page: 416
View: 2578

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Parallel CFD 2004, the sixteenth international conference on Parallel Computational Fluid Dynamics and other modern scientific domains, has been held since May 24th till May 27th, 2004 in Las Palmas de Gran Canaria, Spain. The specialized, high-level Parallel CFD conferences are organised on travelling locations all over the world, yearly because of multidisciplinary subject of parallel CFD and its rapidly evolving nature. The conference featured 8 invited lectures, 3 Mini Symposia, contributed papers and one Tutorial & Short Course. More than 80 multi-disciplinary presentations of the Parallel CFD had been presented, with participants from 17 countries. The sessions involved contributed papers on many diverse subjects including turbulence, complex flows, unstructured and adaptive grids, industrial applications, developments in software tools and environments as parallel optimization tools. This Book presents an up-to-date overview of the state of the art in parallel computational fluid dynamics. - Report on current research in the field. - Researchers around the world are included. - Subject is important to all interested in solving large fluid dynamics problems. - It is of interest to researchers in computer science, engineering and physical sciences. - It is an interdisciplinary activity. Contributions include scientists with a variety of backgrounds. - It is an area which is rapidly changing.

p- and hp- Finite Element Methods

Theory and Applications in Solid and Fluid Mechanics
Author: C. Schwab
Publisher: Clarendon Press
ISBN: 9780198503903
Category: Computers
Page: 386
View: 1917

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The finite element method (FEM) is a numerical procedure for solving differential equations. Ever-increasing computing power means that engineers and applied mathematicians are seeking more complicated and sophisticated numerical methods to obtain progressively more accurate answers to problems in solid and fluid mechanics. The p- and hp- finite element methods are just such methods, and are therefore of great current interest. This book is the first to cover comprehensively the mathematical underpinnings of hp-FEM in one and two dimensions and pays particular attention to its applications in engineering.

Numerical Methods for Stochastic Partial Differential Equations with White Noise

Author: Zhongqiang Zhang,George Em Karniadakis
Publisher: Springer
ISBN: 3319575112
Category: Mathematics
Page: 394
View: 8826

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This book covers numerical methods for stochastic partial differential equations with white noise using the framework of Wong-Zakai approximation. The book begins with some motivational and background material in the introductory chapters and is divided into three parts. Part I covers numerical stochastic ordinary differential equations. Here the authors start with numerical methods for SDEs with delay using the Wong-Zakai approximation and finite difference in time. Part II covers temporal white noise. Here the authors consider SPDEs as PDEs driven by white noise, where discretization of white noise (Brownian motion) leads to PDEs with smooth noise, which can then be treated by numerical methods for PDEs. In this part, recursive algorithms based on Wiener chaos expansion and stochastic collocation methods are presented for linear stochastic advection-diffusion-reaction equations. In addition, stochastic Euler equations are exploited as an application of stochastic collocation methods, where a numerical comparison with other integration methods in random space is made. Part III covers spatial white noise. Here the authors discuss numerical methods for nonlinear elliptic equations as well as other equations with additive noise. Numerical methods for SPDEs with multiplicative noise are also discussed using the Wiener chaos expansion method. In addition, some SPDEs driven by non-Gaussian white noise are discussed and some model reduction methods (based on Wick-Malliavin calculus) are presented for generalized polynomial chaos expansion methods. Powerful techniques are provided for solving stochastic partial differential equations. This book can be considered as self-contained. Necessary background knowledge is presented in the appendices. Basic knowledge of probability theory and stochastic calculus is presented in Appendix A. In Appendix B some semi-analytical methods for SPDEs are presented. In Appendix C an introduction to Gauss quadrature is provided. In Appendix D, all the conclusions which are needed for proofs are presented, and in Appendix E a method to compute the convergence rate empirically is included. In addition, the authors provide a thorough review of the topics, both theoretical and computational exercises in the book with practical discussion of the effectiveness of the methods. Supporting Matlab files are made available to help illustrate some of the concepts further. Bibliographic notes are included at the end of each chapter. This book serves as a reference for graduate students and researchers in the mathematical sciences who would like to understand state-of-the-art numerical methods for stochastic partial differential equations with white noise.

Mixed and Hybrid Finite Element Methods

Author: Franco Brezzi,Michel Fortin
Publisher: Springer Science & Business Media
ISBN: 1461231728
Category: Mathematics
Page: 350
View: 7634

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Research on non-standard finite element methods is evolving rapidly and in this text Brezzi and Fortin give a general framework in which the development is taking place. The presentation is built around a few classic examples: Dirichlet's problem, Stokes problem, Linear elasticity. The authors provide with this publication an analysis of the methods in order to understand their properties as thoroughly as possible.

Computational Fluid Dynamics

A Practical Approach
Author: Jiyuan Tu,Guan-Heng Yeoh,Chaoqun Liu
Publisher: Butterworth-Heinemann
ISBN: 0081012446
Category: Technology & Engineering
Page: 498
View: 3262

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Computational Fluid Dynamics: A Practical Approach, Third Edition, is an introduction to CFD fundamentals and commercial CFD software to solve engineering problems. The book is designed for a wide variety of engineering students new to CFD, and for practicing engineers learning CFD for the first time. Combining an appropriate level of mathematical background, worked examples, computer screen shots, and step-by-step processes, this book walks the reader through modeling and computing, as well as interpreting CFD results. This new edition has been updated throughout, with new content and improved figures, examples and problems. Includes a new chapter on practical guidelines for mesh generation Provides full coverage of high-pressure fluid dynamics and the meshless approach to provide a broader overview of the application areas where CFD can be used Includes online resources with a new bonus chapter featuring detailed case studies and the latest developments in CFD


Modélisation Mathématique Et Analyse Numérique : M2N.. Mathematical modelling and numerical analysis
Author: EDP Sciences
Publisher: N.A
Category: Numerical analysis
Page: N.A
View: 6694

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Numerical Analysis: Historical Developments in the 20th Century

Author: C. Brezinski,L. Wuytack
Publisher: Elsevier
ISBN: 0444598588
Category: Mathematics
Page: 512
View: 8571

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Numerical analysis has witnessed many significant developments in the 20th century. This book brings together 16 papers dealing with historical developments, survey papers and papers on recent trends in selected areas of numerical analysis, such as: approximation and interpolation, solution of linear systems and eigenvalue problems, iterative methods, quadrature rules, solution of ordinary-, partial- and integral equations. The papers are reprinted from the 7-volume project of the Journal of Computational and Applied Mathematics on '/homepage/sac/cam/na2000/index.htmlNumerical Analysis 2000'. An introductory survey paper deals with the history of the first courses on numerical analysis in several countries and with the landmarks in the development of important algorithms and concepts in the field.

Numerical Analysis and Optimization

An Introduction to Mathematical Modelling and Numerical Simulation
Author: Grégoire Allaire
Publisher: Oxford University Press, USA
Category: Mathematics
Page: 455
View: 926

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Based on the Author's teaching notes at the Ecole Polytechnique,iNumerical Analysis and Optimization/i familiarises students with existingmathematical models (often partial differential equations) and their methods ofnumerical solution and optimization. The role of modelling and scientificcomputing has increased dramatically over recent years, and new applications ofmathematical models have emerged in Biology, Environmental Science, Finance,Medicine, and Social Science, as well as the classical applications inChemistry, Mechanics and Physics.Including numerous exercises and examples, this is an ideal text for advancedundergraduates and graduates and researchers in Applied Mathematics,Engineering, Computer Science, and the Physical Sciences.

Computational Hydraulics

An Introduction
Author: Cornelis B. Vreugdenhil
Publisher: Springer Science & Business Media
ISBN: 3642955789
Category: Science
Page: 182
View: 7111

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What is Computational Hydraulics? Computational hydraulics is one of the many fields of science in which the application of computers gives rise to a new way of working, which is intermediate between purely theoretical and experimental. It is concerned with simulation ofthe flow of water, together with its consequences, using numerical methods on com puters. There is not a great deal of difference with computational hydrodynamics or computational fluid dynamics, but these terms are too much restricted to the fluid as such. It seems to be typical of practical problems in hydraulics that they are rarely directed to the flow by itself, but rather to some consequence of it, such as forces on obstacles, transport of heat, sedimentation of a channel or decay of a pollutant. All these subjects require very similar numerical methods and this is why they are treated together in this book. Therefore, I have preferred to use the term computational hydraulics. Accordingly, I have attempted to show the wide field of application by giving examples of a great variety of such practical problems. Purpose of the Book It is getting a normal situation that an engineer is required to solve some engineering problem involving fluid flow, using standard and general-purpose computer programs available in many organizations. In many instances, the software has been designed with the claim that no numerical or computer-science expertise is needed in using them.