Chapter 8 Configuring Fluidity - The Applied Modelling and ...

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viii CONTENTS 8.9.3 Relative Error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 8.9.4 Absolute Error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 8.9.5 Max Iterations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 8.9.6 Start from Zero . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 8.9.7 Remove Null Space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 8.9.8 Solver Failures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 8.9.9 Reordering RCM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 8.9.10 Solver Diagnostics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 8.10 Equation of State (EoS) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 8.11 Subgridscale Parameterisations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 8.11.1 GLS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 8.11.2 k-ε Turbulence Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 8.12 Boundary conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 8.12.1 Adding a boundary condition . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 8.12.2 Selecting surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 8.12.3 Boundary condition types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 8.12.4 Special input date for boundary conditions . . . . . . . . . . . . . . . . . . . . 120 8.12.5 Special cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 8.13 Astronomical tidal forcing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122 8.14 Ocean biology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122 8.15 Sediment model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 8.16 Large scale low aspect ratio ocean simulations . . . . . . . . . . . . . . . . . . . . . . . 124 8.16.1 Options that must be switched on . . . . . . . . . . . . . . . . . . . . . . . . . 124 8.16.2 Recommended or optional settings . . . . . . . . . . . . . . . . . . . . . . . . . 125 8.17 Geophysical fluid dynamics problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 8.17.1 Problem type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 8.17.2 Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 8.17.3 Timestepping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 8.17.4 Material/phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 8.18 Mesh adaptivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 8.18.1 Field settings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 8.18.2 General adaptivity options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 8.19 Multiple material/phase models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 8.19.1 Multiple phase models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 8.19.2 Multiple material models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 8.20 Compressible fluid model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 8.20.1 Pressure options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 8.20.2 Density options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 8.20.3 Velocity options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 8.20.4 Restrictions: discretisation options and element pairs . . . . . . . . . . . . . . 135 9 Visualisation and Diagnostics 137 9.1 Visualisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 9.2 Online diagnostics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 9.2.1 Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 9.3 Offline diagnostics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144 9.3.1 vtktools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144 9.3.2 Diagnostic output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144 9.3.3 fltools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144 9.3.4 Useful scripts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 9.3.5 nodecount.py . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 9.4 The stat file . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156 9.4.1 File format . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 9.4.2 Reading .stat files in python . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
CONTENTS ix 9.4.3 Stat file diagnostics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159 9.4.4 Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164 10 Examples 167 10.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 10.2 One dimensional advection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168 10.2.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168 10.2.2 Configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169 10.2.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170 10.2.4 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171 10.3 The lock-exchange . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171 10.3.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171 10.3.2 Configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172 10.3.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172 10.3.4 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173 10.4 Lid-driven cavity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175 10.4.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175 10.4.2 Configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175 10.4.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175 10.4.4 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176 10.5 Backward facing step . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177 10.5.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177 10.5.2 Configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177 10.5.3 Results: 2D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179 10.5.4 Results: 3D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179 10.6 Flow past a sphere: drag calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182 10.6.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182 10.6.2 Configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182 10.6.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183 10.6.4 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184 10.7 Rotating periodic channel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 10.7.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 10.7.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 10.8 Water column collapse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187 10.8.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187 10.8.2 Problem specification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187 10.8.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188 10.8.4 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192 10.9 The restratification following open ocean deep convection . . . . . . . . . . . . . . . . 193 10.9.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 10.9.2 Configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 10.9.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194 10.10 Tides in the Mediterranean Sea . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195 10.10.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195 10.10.2 Configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196 10.10.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196 Bibliography 201 A About this manual 209 A.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209 A.2 Audience and Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209 A.3 Style guide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210 A.3.1 Headings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210
Page 1: Fluidity�Manual Applied Modelling
Page 5 and 6: Contents 1 Getting started 1 1.1 In
Page 7: CONTENTS vii 7.3 The Gmsh format .
Page 11 and 12: List of Figures 2.1 Schematic of co
Page 13 and 14: LIST OF FIGURES xiii 10.8 Schematic
Page 15 and 16: Chapter 1 Getting started 1.1 Intro
Page 17 and 18: 1.2 Obtaining Fluidity 3 The third,
Page 19 and 20: 1.3 Building Fluidity 5 1.2.3.4 Oth
Page 21 and 22: 1.3 Building Fluidity 7 1.3.2.2 Spe
Page 23 and 24: 1.5 Running diamond 9 Signal handli
Page 25 and 26: Chapter 2 Model equations 2.1 How t
Page 27 and 28: 2.3 Fluid equations 13 2.2.2.2 Neum
Page 29 and 30: 2.3 Fluid equations 15 2.3.2.2 Comp
Page 31 and 32: 2.3 Fluid equations 17 2.3.4 Moment
Page 33 and 34: 2.4 Extensions, assumptions and der
Page 39 and 40: Chapter 3 Numerical discretisation
Page 41 and 42: 3.2 Spatial discretisation of the a
Page 59 and 60:
3.2 Spatial discretisation of the a
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3.2 Spatial discretisation of the a
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3.3 The time loop 49 The coupled li
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3.4 Time discretisation of the adve
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3.6 Pressure equation for incompres
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3.7 Velocity and pressure element p
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3.8 Balance pressure 57 3.8 Balance
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3.10 Linear solvers 59 When reachin
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3.11 Algorithm for detectors (Lagra
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Chapter 4 Parameterisations Althoug
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4.1 Generic length scale turbulence
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4.3 Large-Eddy Simulation (LES) 67
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4.3 Large-Eddy Simulation (LES) 69
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Chapter 5 Embedded models The param
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5.1 Biology 73 where kN is the half
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Chapter 6 Adaptive remeshing 6.1 Mo
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6.4 Metric formation 77 By contrast
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6.6 Related topics 79 There are two
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Chapter 7 Mesh generation This chap
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7.2 The triangle format 83 1 Rema
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7.3 The Gmsh format 85 three parts:
Page 101 and 102:
7.6 Decomposing meshes for parallel
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7.9 Non-Fluidity tools 89 7.7 Pseud
Page 105 and 106:
7.9 Non-Fluidity tools 91 7.9.3 Imp
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Chapter 8 Configuring Fluidity 8.1
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8.3 The options tree 95 Figure 8.2:
Page 111 and 112:
8.3 The options tree 97 8.3.4 IO Th
Page 113 and 114:
8.3 The options tree 99 Checkpoint
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8.3 The options tree 101 8.3.5.3 Fi
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8.4 Meshes 103 if t < 4000.0: omega
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8.5 Material/Phase 105 8.4.2.4 Extr
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8.6 Fields 107 dent field). This is
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8.7 Advected quantities: momentum a
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8.7 Advected quantities: momentum a
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8.9 Solution of linear systems 113
Page 129 and 130:
8.10 Equation of State (EoS) 115 8.
Page 131 and 132:
8.11 Subgridscale Parameterisations
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8.12 Boundary conditions 119 8.12.3
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8.12 Boundary conditions 121 • ..
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8.16 Large scale low aspect ratio o
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8.16 Large scale low aspect ratio o
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8.17 Geophysical fluid dynamics pro
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8.18 Mesh adaptivity 129 An Element
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8.19 Multiple material/phase models
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8.19 Multiple material/phase models
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8.20 Compressible fluid model 135 t
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Chapter 9 Visualisation and Diagnos
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9.2 Online diagnostics 139 Gravitat
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9.2 Online diagnostics 141 Absolute
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9.2 Online diagnostics 143 Figure 9
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9.3 Offline diagnostics 145 Program
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9.3 Offline diagnostics 147 Additio
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9.3 Offline diagnostics 149 9.3.3.1
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9.3 Offline diagnostics 151 Script
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9.3 Offline diagnostics 153 TARGET
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9.3 Offline diagnostics 155 Figure
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9.4 The stat file 157 It is also po
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9.4 The stat file 159 9.4.3 Stat fi
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Temperature min fluid .../stat/incl
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9.4 The stat file 163 9.4.3.1 Surfa
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9.4 The stat file 165 ...
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Chapter 10 Examples 10.1 Introducti
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10.2 One dimensional advection 169
Page 185 and 186:
10.3 The lock-exchange 171 10.2.4 E
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10.3 The lock-exchange 173 basic se
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10.4 Lid-driven cavity 175 domain f
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10.5 Backward facing step 177 Figur
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10.5 Backward facing step 179 No-no
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10.5 Backward facing step 181 Evolu
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10.6 Flow past a sphere: drag calcu
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10.7 Rotating periodic channel 185
Page 201 and 202:
10.8 Water column collapse 187 Exam
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10.8 Water column collapse 189 (a)
Page 205 and 206:
10.8 Water column collapse 191 (a)
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10.9 The restratification following
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10.10 Tides in the Mediterranean Se
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Page 213 and 214:
Page 215 and 216:
Bibliography M. T. Ainsworth and J.
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C. J. Cotter, D. A. Ham, and C. C.
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A. Birol Kara, Harley E. Hurlburt,
Page 221 and 222:
J. R. Shewchuk. An introduction to
Page 223 and 224:
Appendix A About this manual A.1 In
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A.3 Style guide 211 The options pro
Page 227 and 228:
A.3 Style guide 213 A.3.8.3 Derivat
Page 229 and 230:
Appendix B Mathematical notation Th
Page 231 and 232:
Appendix C Useful numbers The table
Page 233 and 234:
Appendix D Dimensional analysis D.1
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D.2 Dimensionless parameters 221 Na
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Appendix E The Fluidity Python stat
Page 239 and 240:
E.6 Debugging with an interactive P
Page 241 and 242:
Appendix F External libraries F.1 I
Page 243 and 244:
F.4 Manual install of external libr
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Page 247 and 248:
Page 249 and 250:
Page 251 and 252:
Appendix G Troubleshooting G.1 Back
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Index absorption term . . . . . . .
Page 255:
geostrophic balance . . . . . . . .
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