Doyub Kim Fluid Engine Development.pdf
( 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
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最优化参考讲义（上海交大参考讲义）
详细介绍了最优化方法，是学习最优化的比较好的参考讲义第一章引言第一章引言§1.1最优化问题概述学科简述最优化理论与方法:研究某些数学上定义的问题的最优解,即对于给出的实际问题,从众多的方案中选出最优方案。最优化是一门应用性很强的年轻学科。比如:●工程设计中怎样选择参数,使得设计既满足要求又能降低成本;资源分配中,怎样的分配方案既能满足各方面的基本要求,又能获得好的经济效益:生产计划安排中,选择怎样的计划方案才能提高产值和利润;·原料配比冋题中,怎样确定各种成分的比例才能提高质量、降低成本,最优化问题分类最优化问题分类表分类标志变量个数变量性质约束情况极值个数日标个数函数关系问题性质时间单变量连续无约朿单峰单目标线性确定性静态类型离散随机性多变量函数约束多峰多日标非线性模糊性动态比如:线性规划,非线性规划,随机规划,非光滑规划,多目标规划,整数规划,工作步骤:用最优化方法解决实际问题,一般经过下列步骤1.提出最优化问题,收集有关数据和资料2.建ν最优化问题的数学模型确定变量,列出目标函数和约束条件;3.分析模型,选择合适的最优化方法4.求解,一般通过编制程序,用计算机求最优解5.最优解的检验和实施上述5个步骤常常相互支持、相互制约,在实践中反复交叉进行。模型的三要素:1.变量:最优化问题中待确定的某些量;2.约束条件:求最优解时对变量的某些限制,包括技术上的约束、资源上的约束和时间上的约束等,用等式、不等式、或可行集表示;1.1最优化闩题概述3.目标函数:最优化评价标准的数学描述,一般用最大或最小表示。最优化方法:解析法,直接法,数值解法,二、线性与非线性规划问题例1.1.1[食谱问题设市场上可以买到n种不同的食品,每种食品含有m种营养成分.每单位的笫j种食品售价为c;,且含有第种营养成分为a;设每人每天对第种营养成分的需求量不少于b;,试确定在保证营养的要求下的最经济食谱建立数学模型(1)根据问题的需要设置变量:设每人每天需要各种食品的数量分别为x1,…,xn(2)用所设置的变量把所追求的目标和听受的约束,用数学语言表述出来,得该问题的数学模型:(1.1.3)这里a11表示购买了x;个第种食品所包含的第种营养量,其中min是 minimize的简写,读作“极小化”,s.t.是 subject tol的简写,读作“受限制于”或“约束条件是”。(1.1.1)称为日标函数,(1.1.2)-(1.1.3)称为约束条件例1.1.2[资金使用问题]设有400万元资金,要求4年内使用完,若在一年使用资金x万元,则可得到效益√万元(效益不能再使用),当年不用的资金可存入银行,年利率为10%。试制订出资金的使用规划,以使4年效益总和为最大。显然,不同的使用方案取得的效益总和是不同的。如(1)第一年就把400万元全部用完,则效益总和为√400=20.0(万元)(2)若前三年均不用而存入银行,则第四年把本息和:400×(1.1)3=532.4(万元)全部用完,则效益总和为√52.4-23.07(万元),比第一方案效益大3万元多;(3)若运用最优化方法,可得如下最优方案第年第二年第三年第四年现有资金400342265.1152.8使用金额86.2104.2126.2152.8第一章引言效益总和为√86.2+√104.2+√126.2+√152.8=43.1(万元),是第方案效益总和的两倍多。建立数学模型:设变量x(i-1,2,3,4)分别表示第所使用的资佥数。所追求的目标-4年的效益总和最大,表为+√3+所受到的约束为每年的使用数额既不能为负数又不能超过当年资金拥有数,即第一年00,存在正整数K>0,使得当k>K时,有|(8)-洲0,使得对于任意的k有|)川0,存在正整数K>0,使得当k,l>K时,有|x()-xO川
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