Moukalled F., Mangani L., Darwish M. The finite volume method in computational fluid dynamics. An advanced introduction with OpenFOAM and Matlab (Moukalled F., Mangani L., Darwish M. The finite volume method in computational fluid dynamics. An advanced introduction with OpenFOAM and Matlab.pdf)

Fluid Mechanics and Its ApplicationsF. MoukalledL. ManganiM. DarwishThe FiniteVolume Methodin ComputationalFluid DynamicsAn Advanced Introduction withOpenFOAM® and Matlab®Fluid Mechanics and Its ApplicationsVolume 113Series editorAndré Thess, German Aerospace Center, Institute of EngineeringThermodynamics, Stuttgart, GermanyFounding EditorRené Moreau, Ecole Nationale Supérieure d’Hydraulique de Grenoble,Saint Martin d’Hères Cedex, FranceAims and Scope of the SeriesThe purpose of this series is to focus on subjects in which fluid mechanics plays afundamental role.As well as the more traditional applications of aeronautics, hydraulics, heat andmass transfer etc., books will be published dealing with topics which are currentlyin a state of rapid development, such as turbulence, suspensions and multiphasefluids, super and hypersonic flows and numerical modeling techniques.It is a widely held view that it is the interdisciplinary subjects that will receiveintense scientific attention, bringing them to the forefront of technologicaladvancement.

Fluids have the ability to transport matter and its properties as wellas to transmit force, therefore fluid mechanics is a subject that is particularly open tocross fertilization with other sciences and disciplines of engineering. The subject offluid mechanics will be highly relevant in domains such as chemical, metallurgical,biological and ecological engineering. This series is particularly open to such newmultidisciplinary domains.The median level of presentation is the first year graduate student. Some texts aremonographs defining the current state of a field; others are accessible to final yearundergraduates; but essentially the emphasis is on readability and clarity.More information about this series at http://www.springer.com/series/5980F.

Moukalled L. ManganiM. Darwish•The Finite Volume Methodin Computational FluidDynamicsAn Advanced Introductionwith OpenFOAM® and Matlab®123F. MoukalledDepartment of Mechanical EngineeringAmerican University of BeirutBeirutLebanonM. DarwishDepartment of Mechanical EngineeringAmerican University of BeirutBeirutLebanonL. ManganiEngineering and ArchitectureLucerne University of Applied Scienceand ArtsHorwSwitzerlandISSN 0926-5112ISSN 2215-0056 (electronic)Fluid Mechanics and Its ApplicationsISBN 978-3-319-16873-9ISBN 978-3-319-16874-6 (eBook)DOI 10.1007/978-3-319-16874-6Library of Congress Control Number: 2015939213Springer Cham Heidelberg New York Dordrecht London© Springer International Publishing Switzerland 2016This work is subject to copyright.

All rights are reserved by the Publisher, whether the whole or partof the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations,recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmissionor information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilarmethodology now known or hereafter developed.The use of general descriptive names, registered names, trademarks, service marks, etc. in thispublication does not imply, even in the absence of a specific statement, that such names are exempt fromthe relevant protective laws and regulations and therefore free for general use.The publisher, the authors and the editors are safe to assume that the advice and information in thisbook are believed to be true and accurate at the date of publication. Neither the publisher nor theauthors or the editors give a warranty, express or implied, with respect to the material contained herein orfor any errors or omissions that may have been made.Printed on acid-free paperSpringer International Publishing AG Switzerland is part of Springer Science+Business Media(www.springer.com)PrefaceThe impetus to write this book came about from three sources:The first source was the bi-yearly computational fluid dynamics (CFD) course,which has been offered over the last 15 years at the American University of Beirut(AUB) by both Drs.

Darwish and Moukalled to senior and graduate mechanicalengineering students, a course that focuses on the finite volume method (FVM) andCFD applications.The second source grew over the years to become more significant as it wasnoticed that graduates have started working on increasingly more focused areas andtopics in CFD while becoming less cognizant of the general algorithmic expertisethat earlier students developed. It became clear that there is a need not only to coverthe basis of the numerics at the core of CFD codes but also to discuss the implementation issues to ensure that all students receive a robust understanding of thetechniques they are working on.Finally, the collaborative work in advanced numerics with Prof.

Dr. Manganifrom HSLU, Lucerne, Switzerland, which started during the Ph.D. supervision ofM. Buchmyer (Ph.D.) from TUGraz, provided all the incentive to clarify and detailmuch of the numerical basis of the algorithms used in OpenFOAM®.To this end, it was decided that the book would combine a mix of numerical andimplementation details allowing the reader, if she/he desires, to fully understandand implement a robust and versatile CFD code based on the FVM.This ambitious task was possible only by selecting from the various numericalmethods in each of the topics covered in the book a handful set with which theauthors are intimately familiar. The result is a book that covers intimately all thetopics necessary for the development of a robust CFD code for the simulation offluid flow at all speeds within the framework of the collocated unstructured finitevolume method.The book was also written with the classroom in mind as reflected by the use ofcopious illustrations; the provision of many exercises covering numerics, programming, and applications; the availability of an academic code (in MATLAB®)that imbeds much of the numerics presented in the book; and finally the variousprograms and routines in OpenFOAM®.vviPrefaceThe hope is that as you read through this book, you will share with us theexcitement and intense interest that we have grown to have for this subject.BeirutHorwBeirutJanuary 2015F.

MoukalledL. ManganiM. DarwishAcknowledgmentsIt took nearly two years to complete this book, but much of what went in it waslearned over a much longer period from interaction with numerous people inconferences and academic visits, from answering pertinent questions in our CFDcourses and from our research work. However the enabler for all that is foremost thepatience and kindness of our families.We also wish to acknowledge the support provided to us by our respectiveinstitutionsAmerican University of BeirutBeirut, LebanonLucerne University of Applied Science and ArtsviiContentsPart IFoundation1Introduction .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . .1.1What Is Computational Fluid Dynamics (CFD) .1.2What Is the Finite Volume Method . . . . . . . . .1.3This Book . . . . . . . . . . . . . . . . . . . . . . . . . .1.3.1Foundation . . . . . . . . . . . . . . . . . . .1.3.2Numerics . . . . . . . . . . . . .

. . . . . . .1.3.3Algorithms . . . . . . . . . . . . . . . . . . .1.3.4Applications . . . . . . . . . . . . . . . . . .1.4Closure . . . . . . . . . . . . . . . . . . . . . . . . . . . ...........................................................................................3345567882Review of Vector Calculus . . . . .

. . . . . . . . . . . . . .2.1Introduction . . . . . . . . . . . . . . . . . . . . . . . . .2.2Vectors and Vector Operations . . . . . . . . . . . .2.2.1The Dot Product of Two Vectors . . .2.2.2Vector Magnitude . . . . . . . . . . . . . .2.2.3The Unit Direction Vector . . . . . . . .2.2.4The Cross Product of Two Vectors .

.2.2.5The Scalar Triple Product. . . . . . . . .2.2.6Gradient of a Scalar and DirectionalDerivatives . . . . . . . . . . . . . . . . . . .2.2.7Operations on the Nabla Operator . . .2.2.8Additional Vector Operations . . . . . .2.3Matrices and Matrix Operations . . . . . . . . . . .2.3.1Square Matrices . . . . . . . . . . . . .

. .2.3.2Using Matrices to Describe Systemsof Equations . . . . . . . . . . . . . . . . . .2.3.3The Determinant of a Square Matrix .2.3.4Eigenvectors and Eigenvalues . . . . . .2.3.5A Symmetric Positive-Definite Matrix................................................................................99101111121214..................................................1517192021........................................23232627ixxContents2.3.6Additional Matrix Operations .

. . . .Tensors and Tensor Operations . . . . . . . . . . .Fundamental Theorems of Vector Calculus. . .2.5.1Gradient Theorem for Line Integrals2.5.2Green’s Theorem. . . . . . . . . . . . . .2.5.3Stokes’ Theorem . . . . . . . . . . . . . .2.5.4Divergence Theorem . . . . . . . . .

. .2.5.5Leibniz Integral Rule . . . . . . . . . . .2.6Closure . . . . . . . . . . . . . . . . . . . . . . . . . . .2.7Exercises . . . . . . . . . . . . . . . . . . . . . . . . . .References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2.42.53..................................................................Mathematical Description of Physical Phenomena . .

. . . . .3.1Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.2Classification of Fluid Flows . . . . . . . . . . . . . . . . . .3.3Eulerian and Lagrangian Description of ConservationLaws . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . .3.3.1Substantial Versus Local Derivative . . . . . . .3.3.2Reynolds Transport Theorem . . . . . . . . . . .3.4Conservation of Mass (Continuity Equation). . . . . . . .3.5Conservation of Linear Momentum . . . . .

. . . . . . . . .3.5.1Non-Conservative Form . . . . . . . . . . . . . . .3.5.2Conservative Form . . . . . . . . . . . . . . . . . .3.5.3Surface Forces . . . . . . . . . . . . . . . . . . . . .3.5.4Body Forces . . . . . . . . . . . . . . . . . . . . . . .3.5.5Stress Tensor and the Momentum Equationfor Newtonian Fluids . . . . . . . . . . . . . . . . .3.6Conservation of Energy . . . . . . . . .