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Elements of Computational Fluid Dynamics M. Ramakrishna Department of Aerospace Engineering Indian Institute of Technology Madras Chennai 600 036 India A Golden Jubilee Publication Published 2011 Elements of Computational Fluid Dynamics Ramakrishna Mokkapati, PhD Department of Aerospace Engineering Indian Institute of Technology Madras Chennai 600 036 ISBN 978-93-80689-05-0 Revision Number: TAB20160217 c 2011 by Ramakrishna Mokkapati, Department of Aerospace Engineering Indian Institute of Technology Madras Chennai 600 036 To everyone who has taught me Contents Preface 8 Introduction 16 What is Computational Fluid Dynamics? 16 Modelling the Universe 18 How do we develop models? 22 Example I - Air 24 Example II - A Nozzle 26 Modelling on the Computer 32 Important ideas from this chapter 43 Representations on the Computer 45 Representing Numbers on the Computer 46 Machine Epsilon 50 Representing Matrices and Arrays on the Computer 58 Representing Intervals and Functions on the Computer 64 Vector Algebra 68 Functions as a Basis: Box Functions 74 Box Functions 75 Polynomial on the Interval [0;1] 86 Linear Approximations: Hat Functions 89 Higher Order Approximations 109 Linear Interpolants on an Interval 116 Local Error Estimates of Approximations 119 Representing Derivatives - Finite Differences 125 Differential Equations 141
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