From: Wolfgang Bangerth Date: Thu, 6 Nov 2008 22:39:43 +0000 (+0000) Subject: Write up 2d part. X-Git-Tag: v8.0.0~8404 X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=133e47ca7d8d76ff4d2e8f24aea4953014e47679;p=dealii.git Write up 2d part. git-svn-id: https://svn.dealii.org/trunk@17500 0785d39b-7218-0410-832d-ea1e28bc413d --- 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