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