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( Doyub Kim Fluid Engine Development.pdf )Doyub Kim Fluid Engine Development.pdfTaylor francisTaylor Francis Grouphttp://taylorandfrancis.comT& F Cat #K25519K25519C000— page l-10/21/2016-17:12LUID ENGINEDEVELOPMENTDOYUB KIM(CRC CRC PressTaylor & fiBoca raton london new yorkCRC Press is an imprint of theTaylor francis Group, an informa businessAN AK PETERS BOOKT& F Cat #K25519—K25519C000- page l-10/21/2016—17:12CRC PressTaylor Francis Group6000 Broken Sound parkway nw, suite 300Boca Raton, FL 33487-274@2017 by Taylor Francis Group, LLCCRC Press is an imprint of Taylor Francis Group, an Informa businessNo clain lo original U.S. Government worksPrinted on acid-free paperVersion date: 20161019International Standard book Number -13: 978-1-4987-1992-6(Pack- Book and ebook)This book contains information obtained from authentic and highly regarded sources. Reasonable effortshave been made to publish reliable data and information, but the author and publisher cannot assumeresponsibility for the validily of all materials or the consequences of their use. The authors and publisherhave attempted to trace the copyright holders of all material reproduced in this publication and apologize toc ht holders if permission to publish in this form has not been obtained If any cocht m aterial hnot been acknowledged please write and let us know so we may rectify in any future reprintExcept as permitted under U.S. Copyright L aw, no part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented,including photocopying, microfilming, and recording, or in any information storage or retrieval system,without written permission from tblishTorpermissiontophotocopyorusematerialelectronicallyfromthisworkpleaseaccesswww.copyrightcom(http://www.copyright.com/)orcontacttheCopyrightClearanceceNter,inC.(ccc),222RosewoodDrive, Danvers, MA 01923, 978-750-8400. CCC is a not-for-profit organization that provides licenses andregistration for a variety of users. For organizations that have been granted a photocopy license by the CCC,a separate system of payment has been arranged.Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are usedonly for identification and explanation without intent to infringeLibrary of Congress Cataloging-in-Publication DataNames: Kim, Doyub, author.Title: Fluid engine development/Doyub KimDescription: Boca Raton: Taylor Francis, a CRC title, part of the TaylorFrancis imprint, a member of the taylor Francis group the academicdivision of T&F Informa, plc, [2017] Includes bibliographical referencesnd indIdentifiers: LCCN 2016028981 ISBN 9781498719926(hardback: acid-free paperSubjects: LCSH: Hydrodynamata processing. Fluids--Computer simulaticClassilication: LCC QA911 K485 2017 DDC 532.00285, 66--dc23Lcrecordavailableathttps://icCn.loc.sov/2016028981Visit the Taylor& Francis Webhttp://www.taylorandfrancis.comand the Crc Press Web site athttp!/www.crcpT&FCat#K25519K25519000— page iv-10/21/2016—17:12To my wifeT& F Cat #K25519K25519C000— page v-10/21/2016-1712Taylor francisTaylor Francis Grouphttp://taylorandfrancis.comT& F Cat #K25519K25519C000— page l-10/21/2016-17:12ContentsPresaList of FigureslI1 Basics1.1 Hello. Fluid SinIdulator1.1.1 Defining State1.1.2 Computing Motion1. 1.3 Boundary handling11.4 Visualization11134621.1.5 Final Rcsult1.2 How to read This book121.2.1 Getting the Codes131.2.2 Rcading codcs131. 2.2. 1 Languages131.2.2.2 Source code st131.2.2.3 Naming Conventions141.2.2.4 Constants151.2.2.5 Array151.2.3 Reading math Expressions01.2.3.1 Scalar. Vector and Matrix201.3 Math1.3. 1 Coordinate System211.3.2 Vector211.3.2.1 Basic Operations241.3.2.2 Dot and cross product261.3.2.3 More Operations273.3 Matri1.3.3.1 Basic Matrix Operations1.3.3.2 Sparse Matrix361.3.4 System of Linear Equations371.3.4.1 Direct Methods1.3.4.2 Indirect Methods381. 3.5 Field421.3.5.1 Partial derivative451.3.5.2 GradientT&FCat#K25519—K25519C000— page vll-10/21/2016-17:12Contents1.3.5.3 Divergence481.3.54C511.3.5.5 Laplacian531.3.6 Interpolation561.3.6.1 Nearest point581.3.6.2 Linear Interpolation591.3.6.3 Cat, mull-Rom Spline Interpolation61eometry631. 4.1 Surface671.4.3 Implicit Surface to Explicit Surface1.4.4 Explicit Surface to Implicit Surface1.5 Animation番普721.6 Physics-Based Animation1.6.1 Getting Started771.6. 2 Physics Animation with Example781.6.2. 1 Choosing a Model781. 6. 2.2 Simulation State791.6.2.3 Force and Motion801.6.2. 4 Time Integration871.6. 2.5 Constraints and collisions891.7 Fluid Animation911.7.1 Gravity1.7.2P1.7.3 Viscosity1.7.4 Density Constraint2 Particle-Based Simulation992.1 Seeing the World Like Seurat992 Data Structi2.2.1 Particle System Data1002.2.2 Particle System Example2.2.3 Neighbor1082.2.3.1 Searching Nearby Particlesl092.2.3.2 Caching Neighbors2.3 SOothed Particles116asics2.3.1.1 Kernel1172.3.1.2 Data Model119lerdO1202.3.1.4 Density1212.3.1.5 Differential Operators2.3.2 Dynamics1302.3.2. 1 Solver Over view1312.3.2.2 Pressure gradient Force133T&FCa#K25519—K25519C000— page vil-10/21/2016—17:12Contents2.3.2.3 Viscosity1372.3.2.4 Gravity and Drag Forces1372.3.3 Results and limitations1382.4 Incompressible SPii with Larger Time-Step12.4Predict and correct2.4.2 Implementation2.4.3 Results1472.5 Collision Handling1492.5.1 Defining colliders1502.6 Discussion and further reading1553 Grid-Based simulation1573.1 Pixelating the World1573. 2 Data Structures1573.2.1 Types of grid1593.2.2 Grid System D1663.3 Differential Operators1693.3.1 Finite difference1703.3.2 Gradient1723.3. 3 Divergence1733.3.4 Curl1763.3.5 Lap1783. 4 Fluid simulation1803.4.1 Collision Handling1823.4.1.1 Collider to Signed-Distance Field1823.4.1.2 Boundary Conditions1833.4.2 Advection1873.4.2.1 Semi-Lagrangian Method1883.4.2.2Ing Backg Accurac1923.4.2.3 Improving Interpolation Accuracy1943.4.2.4 Boundary handlingg1963.43G1983.4.4. 1 Solving Diffusion with Forward Euler1993.4.4.2 Stability of diffuusIonSol2013.4.4.3 Solving DiffusiOn with Backward Euler2033.4.4.4 Boundary Handling2083.4.5 Pressure and Incompressibility2113.4.5. 1 Building matrix2143.5 Smoke simulation2203.5.1 Buoyancy Force2223.5.2 Advection and Diffusioll3.6 Fluid with Surface2233.6.1 Defining surfacc on grids233.6.1.1 Tracking the Surface under the Flow263.6.1.2 Reinitializing Signed-Distance Field226T&FCat#K25519—K25519C000— page ix-10/21/2016—17:12