Discontinuous Finite Elements in Fluid Dynamics and Heat Transfer
Discontinuous Finite Elements in Fluid Dynamics and Heat Transfer

Author: Ben Q. Li

Publisher: Springer

Published: 2010-10-22

Total Pages: 0

ISBN-13: 9781849969901

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Over the past several years, significant advances have been made in developing the discontinuous Galerkin finite element method for applications in fluid flow and heat transfer. Certain unique features of the method have made it attractive as an alternative for other popular methods such as finite volume and finite elements in thermal fluids engineering analyses. This book is written as an introductory textbook on the discontinuous finite element method for senior undergraduate and graduate students in the area of thermal science and fluid dynamics. It also can be used as a reference book for researchers and engineers who intend to use the method for research in computational fluid dynamics and heat transfer. A good portion of this book has been used in a course for computational fluid dynamics and heat transfer for senior undergraduate and first year graduate students. It also has been used by some graduate students for self-study of the basics of discontinuous finite elements. This monograph assumes that readers have a basic understanding of thermodynamics, fluid mechanics and heat transfer and some background in numerical analysis. Knowledge of continuous finite elements is not necessary but will be helpful. The book covers the application of the method for the simulation of both macroscopic and micro/nanoscale fluid flow and heat transfer phenomena.

Discontinuous Galerkin Methods
Discontinuous Galerkin Methods

Author: Bernardo Cockburn

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 468

ISBN-13: 3642597211

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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.

The Finite Element Method in Heat Transfer and Fluid Dynamics, Third Edition
The Finite Element Method in Heat Transfer and Fluid Dynamics, Third Edition

Author: J. N. Reddy

Publisher: CRC Press

Published: 2010-04-06

Total Pages: 515

ISBN-13: 1420085980

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As Computational Fluid Dynamics (CFD) and Computational Heat Transfer (CHT) evolve and become increasingly important in standard engineering design and analysis practice, users require a solid understanding of mechanics and numerical methods to make optimal use of available software. The Finite Element Method in Heat Transfer and Fluid Dynamics, Third Edition illustrates what a user must know to ensure the optimal application of computational procedures—particularly the Finite Element Method (FEM)—to important problems associated with heat conduction, incompressible viscous flows, and convection heat transfer. This book follows the tradition of the bestselling previous editions, noted for their concise explanation and powerful presentation of useful methodology tailored for use in simulating CFD and CHT. The authors update research developments while retaining the previous editions’ key material and popular style in regard to text organization, equation numbering, references, and symbols. This updated third edition features new or extended coverage of: Coupled problems and parallel processing Mathematical preliminaries and low-speed compressible flows Mode superposition methods and a more detailed account of radiation solution methods Variational multi-scale methods (VMM) and least-squares finite element models (LSFEM) Application of the finite element method to non-isothermal flows Formulation of low-speed, compressible flows With its presentation of realistic, applied examples of FEM in thermal and fluid design analysis, this proven masterwork is an invaluable tool for mastering basic methodology, competently using existing simulation software, and developing simpler special-purpose computer codes. It remains one of the very best resources for understanding numerical methods used in the study of fluid mechanics and heat transfer phenomena.

The Finite Element Method in Heat Transfer and Fluid Dynamics, Second Edition
The Finite Element Method in Heat Transfer and Fluid Dynamics, Second Edition

Author: J. N. Reddy

Publisher: CRC Press

Published: 2000-12-20

Total Pages: 496

ISBN-13: 9780849323553

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The numerical simulation of fluid mechanics and heat transfer problems is now a standard part of engineering practice. The widespread availability of capable computing hardware has led to an increased demand for computer simulations of products and processes during their engineering design and manufacturing phases. The range of fluid mechanics and heat transfer applications of finite element analysis has become quite remarkable, with complex, realistic simulations being carried out on a routine basis. The award-winning first edition of The Finite Element Method in Heat Transfer and Fluid Dynamics brought this powerful methodology to those interested in applying it to the significant class of problems dealing with heat conduction, incompressible viscous flows, and convection heat transfer. The Second Edition of this bestselling text continues to provide the academic community and industry with up-to-date, authoritative information on the use of the finite element method in the study of fluid mechanics and heat transfer. Extensively revised and thoroughly updated, new and expanded material includes discussions on difficult boundary conditions, contact and bulk nodes, change of phase, weighted-integral statements and weak forms, chemically reactive systems, stabilized methods, free surface problems, and much more. The Finite Element Method in Heat Transfer and Fluid Dynamics offers students a pragmatic treatment that views numerical computation as a means to an end and does not dwell on theory or proof. Mastering its contents brings a firm understanding of the basic methodology, competence in using existing simulation software, and the ability to develop some simpler, special purpose computer codes.

Transport Phenomena in Micro Process Engineering
Transport Phenomena in Micro Process Engineering

Author: Norbert Kockmann

Publisher: Springer Science & Business Media

Published: 2007-11-12

Total Pages: 382

ISBN-13: 3540746188

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In this book, the fundamentals of chemical engineering are presented with respect to applications in micro system technology, microfluidics, and transport processes within microstructures. Special features of the book include the state-of-the-art in micro process engineering, a detailed treatment of transport phenomena for engineers, and a design methodology from transport effects to economic considerations.

Computational Cardiovascular Mechanics
Computational Cardiovascular Mechanics

Author: Julius M. Guccione

Publisher: Springer Science & Business Media

Published: 2010-01-08

Total Pages: 335

ISBN-13: 1441907300

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Computational Cardiovascular Mechanics provides a cohesive guide to creating mathematical models for the mechanics of diseased hearts to simulate the effects of current treatments for heart failure. Clearly organized in a two part structure, this volume discusses various areas of computational modeling of cardiovascular mechanics (finite element modeling of ventricular mechanics, fluid dynamics) in addition to a description an analysis of the current applications used (solid FE modeling, CFD). Edited by experts in the field, researchers involved with biomedical and mechanical engineering will find Computational Cardiovascular Mechanics a valuable reference.

Building Bridges: Connections and Challenges in Modern Approaches to Numerical Partial Differential Equations
Building Bridges: Connections and Challenges in Modern Approaches to Numerical Partial Differential Equations

Author: Gabriel R. Barrenechea

Publisher: Springer

Published: 2016-10-03

Total Pages: 443

ISBN-13: 3319416405

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This volume contains contributed survey papers from the main speakers at the LMS/EPSRC Symposium “Building bridges: connections and challenges in modern approaches to numerical partial differential equations”. This meeting took place in July 8-16, 2014, and its main purpose was to gather specialists in emerging areas of numerical PDEs, and explore the connections between the different approaches. The type of contributions ranges from the theoretical foundations of these new techniques, to the applications of them, to new general frameworks and unified approaches that can cover one, or more than one, of these emerging techniques.

Materials Characterisation VI
Materials Characterisation VI

Author: C. A. Brebbia

Publisher: WIT Press

Published: 2013

Total Pages: 365

ISBN-13: 1845647203

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This book contains papers to be presented at the Sixth International Conference on the topic. Materials modelling and characterisation have become ever more closely intertwined. Characterisation, in essence, connects the abstract material model with the real-world behaviour of the material in question. Characterisation of complex materials often requires a combination of experimental and computational techniques. The conference is convened biennially to facilitate the sharing of recent work between researchers who use computational methods, those who perform experiments, and those who do both, in all areas of materials characterisation.The papers cover such topics as: Computational models and experiments; Mechanical characterisation and testing; Micro and macro materials characterisation; Corrosion problems; Innovative experimental technologies; Recycled materials; Thermal analysis; Advances in composites; Cementitious materials; Structural health monitoring; Energy materials.

Automated Solution of Differential Equations by the Finite Element Method
Automated Solution of Differential Equations by the Finite Element Method

Author: Anders Logg

Publisher: Springer Science & Business Media

Published: 2012-02-24

Total Pages: 723

ISBN-13: 3642230997

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This book is a tutorial written by researchers and developers behind the FEniCS Project and explores an advanced, expressive approach to the development of mathematical software. The presentation spans mathematical background, software design and the use of FEniCS in applications. Theoretical aspects are complemented with computer code which is available as free/open source software. The book begins with a special introductory tutorial for beginners. Following are chapters in Part I addressing fundamental aspects of the approach to automating the creation of finite element solvers. Chapters in Part II address the design and implementation of the FEnicS software. Chapters in Part III present the application of FEniCS to a wide range of applications, including fluid flow, solid mechanics, electromagnetics and geophysics.

Numerical Methods for Conservation Laws
Numerical Methods for Conservation Laws

Author: Jan S. Hesthaven

Publisher: SIAM

Published: 2018-01-30

Total Pages: 571

ISBN-13: 1611975093

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Conservation laws are the mathematical expression of the principles of conservation and provide effective and accurate predictive models of our physical world. Although intense research activity during the last decades has led to substantial advances in the development of powerful computational methods for conservation laws, their solution remains a challenge and many questions are left open; thus it is an active and fruitful area of research. Numerical Methods for Conservation Laws: From Analysis to Algorithms: offers the first comprehensive introduction to modern computational methods and their analysis for hyperbolic conservation laws, building on intense research activities for more than four decades of development; discusses classic results on monotone and finite difference/finite volume schemes, but emphasizes the successful development of high-order accurate methods for hyperbolic conservation laws; addresses modern concepts of TVD and entropy stability, strongly stable Runge-Kutta schemes, and limiter-based methods before discussing essentially nonoscillatory schemes, discontinuous Galerkin methods, and spectral methods; explores algorithmic aspects of these methods, emphasizing one- and two-dimensional problems and the development and analysis of an extensive range of methods; includes MATLAB software with which all main methods and computational results in the book can be reproduced; and demonstrates the performance of many methods on a set of benchmark problems to allow direct comparisons. Code and other supplemental material are available online at www.siam.org/books/cs18.