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

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10 Getting started If the make command successfully completed, there will be an executable program diamond in the bin/ directory. Running diamond is now as simple as typing: /bin/diamond If the make install command completed and a directory which executable programs were installed into to the PATH environment variable, one may also be able to run diamond simply by typing diamond at the command line from any directory on your system. This may also be possible if the Diamond package for Ubuntu or Debian is installed by running: sudo apt-get install diamond Note that installing Diamond on a system-wide basis will require superuser privileges on the system. 1.6 Working with the output Once Fluidity has been built and run, result files will be generated, that will need visualising and post-processing. These data are stored in VTK files, one per output dump. How these files can be visualised and post-processed is covered in detail in chapter 9. As well as visualisation, another important output resource is the stat file, described in detail in section 9.4, which contains data from the model collected at run time. See the AMCG website for more information.
Chapter 2 Model equations 2.1 How to navigate this chapter This chapter covers the fluid and associated field equations modeled by Fluidity. problem underlying equations boundary conditions other considerations scalar advection 2.2.1, 2.2.1.1 2.2.2.1, 2.2.2.2 scalar advection-diffusion 2.2.1, 2.2.1.2 momentum equation 2.3 2.3.4.1, 2.3.4.2, 2.3.4.3, 2.3.4.4 2.4 The material covered in this chapter is dealt with in great detail in Batchelor [1967] and Landau and Lifshitz [1987]. Cushman-Roisin [1994] is also a useful reference. 2.2 Advection–Diffusion equation 2.2.1 General equation The general form the equation that governs the evolution of a scalar field c (e.g., passive tracer, species concentration, temperature, salinity) is ∂c + ∇ · (uc) = ∇ · (κ∇c) − σc + F, (2.1) ∂t where u = (u, v, w) T is the velocity vector, κ is the diffusivity (tensor), σ is an absorption coefficient (−σc is sometimes termed Rayleigh or linear friction) and F represents any source or reaction terms. 2.2.1.1 Advection The advection term in (2.1), given by ∇ · (uc) = u · ∇c + (∇ · u)c, (2.2) expresses the transport of the scalar quantity c in the flow field u. Note that for an incompressible flow ∇ · u = 0 (see section 2.3.3) resulting in the second term on the right hand side of (2.2) dropping out. However, there may be numerical reasons why the discrete velocity field is not exactly 11
Page 1: Fluidity�Manual Applied Modelling
Page 5 and 6: Contents 1 Getting started 1 1.1 In
Page 7 and 8: CONTENTS vii 7.3 The Gmsh format .
Page 9 and 10: CONTENTS ix 9.4.3 Stat file diagnos
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: 1.5 Running diamond 9 Signal handli
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 63 and 64: 3.3 The time loop 49 The coupled li
Page 65 and 66: 3.4 Time discretisation of the adve
Page 67 and 68: 3.6 Pressure equation for incompres
Page 69 and 70: 3.7 Velocity and pressure element p
Page 71 and 72: 3.8 Balance pressure 57 3.8 Balance
Page 73 and 74: 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:
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7.6 Decomposing meshes for parallel
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7.9 Non-Fluidity tools 89 7.7 Pseud
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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:
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8.3 The options tree 97 8.3.4 IO Th
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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
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8.10 Equation of State (EoS) 115 8.
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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
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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
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10.8 Water column collapse 187 Exam
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10.8 Water column collapse 189 (a)
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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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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,
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J. R. Shewchuk. An introduction to
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Appendix A About this manual A.1 In
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A.3 Style guide 211 The options pro
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A.3 Style guide 213 A.3.8.3 Derivat
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Appendix B Mathematical notation Th
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Appendix C Useful numbers The table
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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
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E.6 Debugging with an interactive P
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Appendix F External libraries F.1 I
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F.4 Manual install of external libr
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Appendix G Troubleshooting G.1 Back
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Index absorption term . . . . . . .
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geostrophic balance . . . . . . . .
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