From f805ef9d088e87a1c714c3debb9c7b91b2020cac Mon Sep 17 00:00:00 2001 From: bangerth Date: Thu, 6 Nov 2008 22:39:43 +0000 Subject: [PATCH] Write up 2d part. git-svn-id: https://svn.dealii.org/trunk@17500 0785d39b-7218-0410-832d-ea1e28bc413d --- deal.II/examples/step-31/doc/results.dox | 150 ++++++++++++++++++ .../step-31/doc/step-31.2d.grid.00.png | Bin 0 -> 50532 bytes .../step-31/doc/step-31.2d.grid.01.png | Bin 0 -> 71276 bytes .../step-31/doc/step-31.2d.grid.02.png | Bin 0 -> 93659 bytes .../step-31/doc/step-31.2d.grid.03.png | Bin 0 -> 109770 bytes .../step-31/doc/step-31.2d.grid.04.png | Bin 0 -> 135218 bytes .../step-31/doc/step-31.2d.grid.05.png | Bin 0 -> 145506 bytes .../step-31/doc/step-31.2d.grid.06.png | Bin 0 -> 160584 bytes .../step-31/doc/step-31.2d.grid.07.png | Bin 0 -> 171903 bytes .../step-31/doc/step-31.2d.solution.00.png | Bin 0 -> 6587 bytes .../step-31/doc/step-31.2d.solution.01.png | Bin 0 -> 16188 bytes .../step-31/doc/step-31.2d.solution.02.png | Bin 0 -> 26758 bytes .../step-31/doc/step-31.2d.solution.03.png | Bin 0 -> 36056 bytes .../step-31/doc/step-31.2d.solution.04.png | Bin 0 -> 43289 bytes .../step-31/doc/step-31.2d.solution.05.png | Bin 0 -> 59270 bytes .../step-31/doc/step-31.2d.solution.06.png | Bin 0 -> 74005 bytes .../step-31/doc/step-31.2d.solution.07.png | Bin 0 -> 85101 bytes 17 files changed, 150 insertions(+) create mode 100644 deal.II/examples/step-31/doc/step-31.2d.grid.00.png create mode 100644 deal.II/examples/step-31/doc/step-31.2d.grid.01.png create mode 100644 deal.II/examples/step-31/doc/step-31.2d.grid.02.png create mode 100644 deal.II/examples/step-31/doc/step-31.2d.grid.03.png create mode 100644 deal.II/examples/step-31/doc/step-31.2d.grid.04.png create mode 100644 deal.II/examples/step-31/doc/step-31.2d.grid.05.png create mode 100644 deal.II/examples/step-31/doc/step-31.2d.grid.06.png create mode 100644 deal.II/examples/step-31/doc/step-31.2d.grid.07.png create mode 100644 deal.II/examples/step-31/doc/step-31.2d.solution.00.png create mode 100644 deal.II/examples/step-31/doc/step-31.2d.solution.01.png create mode 100644 deal.II/examples/step-31/doc/step-31.2d.solution.02.png create mode 100644 deal.II/examples/step-31/doc/step-31.2d.solution.03.png create mode 100644 deal.II/examples/step-31/doc/step-31.2d.solution.04.png create mode 100644 deal.II/examples/step-31/doc/step-31.2d.solution.05.png create mode 100644 deal.II/examples/step-31/doc/step-31.2d.solution.06.png create mode 100644 deal.II/examples/step-31/doc/step-31.2d.solution.07.png diff --git a/deal.II/examples/step-31/doc/results.dox b/deal.II/examples/step-31/doc/results.dox index b0f079ce04..8e502905f1 100644 --- a/deal.II/examples/step-31/doc/results.dox +++ b/deal.II/examples/step-31/doc/results.dox @@ -1,5 +1,155 @@

Results

+

Results in 2d

+ +When you run the program in 2d, the output will look something like +this: + +
+Number of active cells: 64 (on 3 levels)
+Number of degrees of freedom: 3041 (2187+125+729)
+
+Timestep 0:  t=0, dt=0
+   Assembling...
+   Rebuilding Stokes preconditioner...
+   Solving...
+   0 GMRES iterations for Stokes subsystem.
+   11 CG iterations for temperature.
+   Temperature range: -0.574475 4.20612
+
+Number of active cells: 288 (on 4 levels)
+Number of degrees of freedom: 12379 (8943+455+2981)
+
+Timestep 0:  t=0, dt=2.08333
+   Assembling...
+   Rebuilding Stokes preconditioner...
+   Solving...
+   0 GMRES iterations for Stokes subsystem.
+   12 CG iterations for temperature.
+   Temperature range: -0.449202 1.92021
+
+Number of active cells: 1296 (on 5 levels)
+Number of degrees of freedom: 51497 (37305+1757+12435)
+
+Timestep 0:  t=0, dt=1.04167
+   Assembling...
+   Rebuilding Stokes preconditioner...
+   Solving...
+   0 GMRES iterations for Stokes subsystem.
+   11 CG iterations for temperature.
+   Temperature range: -0.423543 0.720648
+
+Number of active cells: 5104 (on 6 levels)
+Number of degrees of freedom: 194273 (140913+6389+46971)
+
+Timestep 0:  t=0, dt=0.520833
+   Assembling...
+   Rebuilding Stokes preconditioner...
+   Solving...
+   0 GMRES iterations for Stokes subsystem.
+   12 CG iterations for temperature.
+   Temperature range: -0.228566 0.423852
+
+Timestep 1:  t=0.260417, dt=0.260417
+   Assembling...
+   Solving...
+   63 GMRES iterations for Stokes subsystem.
+   11 CG iterations for temperature.
+   Temperature range: -0.280384 0.640062  
+
+...
+
+
+ +In the beginning we refine the mesh several times adaptively and +always return to time step zero to restart on the newly refined +mesh. Only then do we start the actual time iteration. + +The program runs for a while. The temperature field for time steps 0, +500, 1000, 1500, 2000, 3000, 4000, and 5000 looks like this (note that +the color scale used for the temperature is not always the same): + + + + + + + + + + + + + + + +
+ @image html "step-31.2d.solution.00.png" "" width=22% + + @image html "step-31.2d.solution.01.png" "" width=22% + + @image html "step-31.2d.solution.02.png" "" width=22% + + @image html "step-31.2d.solution.03.png" "" width=22% +
+ @image html "step-31.2d.solution.04.png" "" width=22% + + @image html "step-31.2d.solution.05.png" "" width=22% + + @image html "step-31.2d.solution.06.png" "" width=22% + + @image html "step-31.2d.solution.07.png" "" width=22% +
+ +As can be seen, we have three heat sources that heat fluid and +therefore produce a buoyancy effect that lets hots pockets of fluid +rise up and swirl around. By a chimney effect, the three streams are +pressed together by fluid that comes from the outside and wants to +join the updraft party. Note that because the fluid is initially at +rest, those parts of the fluid that were initially over the sources +receive a longer heating time than that fluid that is later dragged +over the source by the fully developed flow field. It is therefore +hotter, a fact that can be seen in the red tips of the three +plumes. Note also the relatively fine features of the flow field, a +result of the sophisticated transport stabilization of the temperature +equation we have chosen. + +In addition to the pictures above, the following ones show the +adaptive mesh and the flow field at the same time steps: + + + + + + + + + + + + + + + +
+ @image html "step-31.2d.grid.00.png" "" width=22% + + @image html "step-31.2d.grid.01.png" "" width=22% + + @image html "step-31.2d.grid.02.png" "" width=22% + + @image html "step-31.2d.grid.03.png" "" width=22% +
+ @image html "step-31.2d.grid.04.png" "" width=22% + + @image html "step-31.2d.grid.05.png" "" width=22% + + @image html "step-31.2d.grid.06.png" "" width=22% + + @image html "step-31.2d.grid.07.png" "" width=22% +
+ +

Numerical experiments to determine optimal parameters

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