(Cambridge Texts in Applied Mathematics ) Sam Howison-Practical Applied Mathematics Modelling, Analysis, Approximation-Cambridge University Press (2005).pdf

Practical Applied Mathematics
Modelling, Analysis, Approximation
Sam Howison
OCIAM
Mathematical Institute
Oxford University
October 10, 2003
2
Contents
1 Introduction 9
What is modelling/why model? ................. 9
....................... 9
......................... 9
I Modelling techniques 11
2 The basics of modelling 13
Introduction ............................ 13
?................. 14
Principles of modelling . . . ................... 16
Example:inviscidfluidmechanics............ 17
Example:viscousfluids.................. 18
......................... 21
Conclusion ............................. 22
3Unitsanddimensions 25
Introduction ............................ 25
....................... 25
Example:heatflow.................... 27
................. 28
4 Dimensional analysis 39
...................... 39
Example:advection-diffusion.............. 39
Example: the damped pendulum ............ 43
Example:beamsandstrings............... 45
–Stokesequations................... 47
Waterinthebathtub................... 50
’sPi-theorem.................... 51
3
4 CONTENTS
.............................. 53
5 Case study: hair modelling and cable laying 61
–Bernoullimodelforabeam............. 61
Hair modelling .......................... 63
-laying............................ 64
Modelling and analysis ...................... 65
Boundary conditions . . ................. 67
Effectiveforcesandnondimensionalisation....... 67
6 Case study: the thermistor 1 73
............................ 73
Asimplemodel...................... 73
...................... 75