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gtspring2009:schedule:chflow1 [2009/01/25 18:32]
dspieker 		gtspring2009:schedule:chflow1 [2010/02/02 07:55] (current)
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 ===== Important concepts ===== ===== Important concepts =====
- 
- 
 ==== FlowField ==== ==== FlowField ====
  
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 scripts add the laminar flow back on by default. scripts add the laminar flow back on by default.
  
- +**Note: I moved the rest of this class tutorial ​into the ** [[docs:tutorial|channelflow ​tutorial]]. //John Gibson 2009-01-29//
-==== Channelflow utilities ==== +
- +
-FlowFields are binary file representations of velocity fields. +
- +
-Channelflow utilities are programs that operate on FlowField files or directories +
-of FlowField files saved at regular intervals. +
- +
-Examples: +
-^ utility ^ action ^ +
-| fieldprops ​   | print out properties of field: norms, symmetries, etc. | +
-| fieldplots ​   | extract 2D slices of a velocity field for plotting ​    | +
-| addfields ​    | compute u' = sum a_n u_n and save to disk              | +
-| couette ​      | integrate an initial condition, save results to disk   ​| ​  +
-| seriesprops ​  | compute statistics of saved fields ​                    | +
-| makebasis ​    | Gram-Schmidt orthogonalize a set of fields ​            | +
-| projectseries | project saved data onto basis set                      | +
-| findorbit ​    | compute equilibria, traveling waves, periodic orbits ​  | +
-| arnoldi ​      | compute eigenvalues of solutions via Arnoldi iteration | +
- +
-The utilities are stand-alone command-line programs that are run from +
-the Unix shell. You can get brief built-in help information on each +
-utility by running it with a -h or --help option. For example, running +
-"​couette --help"​ produces +
- +
-  gibson@akbar$ couette --help +
-  couette : +
-        integrate an initial condition and save velocity fields to disk. +
- +
-  options : +
-    -T0       ​--T0 ​          <​real> ​  ​default == 0       start time +
-    -T1       ​--T1 ​          <​real> ​  ​default == 100     end time +
-    -vdt      --variabledt ​                              ​adjust dt for CFL +
-    -dt       ​--dt ​          <​real> ​  ​default == 0.03125 timestep +
-    -dtmin ​   --dtmin ​       <​real> ​  ​default == 0.001   ​minimum time step +
-    -dtmax ​   --dtmax ​       <​real> ​  ​default == 0.05    maximum time step +
-    -dT       ​--dT ​          <​real> ​  ​default == 1       save interval +
-    -CFLmin ​  ​--CFLmin ​      <​real> ​  ​default == 0.4     ​minimum CFL number +
-    -CFLmax ​  ​--CFLmax ​      <​real> ​  ​default == 0.6     ​maximum CFL number +
-    -ts       ​--timestepping <​string>​ default == sbdf3   ​timestepping algorithm +
-    ... +
-     ​-p ​       --pressure ​                               print pressure grad +
-    <​flowfield> ​     (trailing arg 1)                    initial condition +
- +
-The built-in help gives a brief description ​of each utility'​s purpose +
-and a list of its command-line options and arguments. Channelflow +
-utilities are invoked at the command line with syntax like +
- +
-   ​utility -opt1 value -opt2 value -flag1 arg3 arg2 arg1 +
- +
-or concretely +
- +
-   ​couette -T0 0 -T1 400 -vdt -dt 0.02 -ts sbdf4 u0.ff +
- +
-Utilities often store data at regular intervals dT into a output directory, specified with  +
--T0, -T1, and -dT, and -o options. E.g.  +
- +
-   ​couette -T0 0 -T1 400 -dt 0.02 -dT 2.0 -o data/ u0.ff +
- +
-integrates ​the flow from t=T0 to t=T1 with timestep dt=0.02 and stores a time series of  +
-velocity fields at intervals dT=2.0 in the ''​data/''​ directory. The velocity fields have  +
-filenames  +
- +
-  data/​u0.ff +
-  data/​u1.ff +
-  etc. +
- +
-where the label is the time t = T0 + n dT. If T0 or dT is not an integer, the label is rounded  +
-to three decimal places. +
- +
-For utilities that //read// time series of velocity fields, you need to specify the same  +
-(or compatible) time intervals. For the most part, the default dT=1 is a good, simple interval.  +
- +
-Most utilities echo the command-line arguments into a file //​utilityname//​.args,​ to help you keep  +
-track of what you've done. +
- +
-Reynolds number defaults to 400. +
- +
- +
-===== Example calculations ===== +
-==== Computing a 1d unstable manifold ==== +
-    +
-The Nagata (1990) "​lower-branch"​ equilibrium has a one-dimensional unstable manifold. +
-Here we compute the unstable manifold by integrating two 1d trajectories  +
- +
-<​latex>​ +
-u_{\pm}(x,​t) = f^t(u_{LB} \pm v_{LB}), t \in [0, \infty] +
-</​latex>​ +
- +
-using several channelflow utilities:  +
- +
-  ​* ''​fieldprops''​ +
-  ​* ''​arnoldi''​ +
-  * ''​addfields''​ +
-  * ''​couette''​ +
-  * ''​seriesprops''​ +
-  * ''​makebasis''​ +
-  * ''​projectseries''​ +
-\\ +
-\\ +
-1. Download the solution from the [[http://​www.channelflow.org/​database|channelflow ​database]]  +
- +
-   wget http://​channelflow.org/database/a1.14_g2.5_Re400/​LB.ff +
-\\ +
-\\ +
-2. Examine the properties of the lower-branch solution with ''​fieldprops''​ +
- +
-   ​fieldprops -g uLB +
-\\ +
-\\ +
-3. Plot the LB with "​fieldplots"​ and matlab script "​plotbox"​ (bad  +
- +
-   ​fieldplots -o plot uLB +
-    +
-then within Matlab, ''​plotbox('​LB'​)''​. +
-\\ +
-\\ +
-\\ +
-4. Compute the eigenfunctions with ''​arnoldi''​ (skip this?) +
- +
-   ​arnoldi --flow LB.ff +
- +
-This produces a set of (approximate) eigenfunctions ''​ef1.ff,​ ef2.ff, ...''​ and a  +
-file of eigenvalues ''​lambda.asc''​.  +
-\\ +
-\\ +
-\\ +
-5. Perturb along the unstable eigenfunction with ''​addfields''​ +
- +
-  addfields 1 LB  0.01 ef1  LBp01ef1 +
-  addfields 1 LB -0.01 ef1  LBm01ef1 +
-\\ +
- +
-8-) I think that both instances of "​LB"​ here should be replaced by "​LB.ff"​ and similarly +
-both instances of "​ef1"​ should be replaced with "​ef1.ff"​ - Dustin +
- +
-\\ +
-6. Integrate the perturbations with ''​couette''​ +
- +
-  couette -T0 0 -T1 400 -o data-LBp01 LBp01ef1 +
-  couette -T1 0 -T1 400 -0 data-LBm01 LBm01ef1 +
-\\ +
- +
-8-) I think it should be "​-T0"​ in the second line here instead of "​-T1"​. ​ It +
-may not make a difference, because I didn't run it both ways, but "​-O"​ might +
-need to be replaced by "​-o"​. -Dustin +
- +
-\\ +
-7. Produce input vs dissipation curves for perturbations with ''​seriesprops''​ +
- +
-   ​seriesprops -T0 0 -T1 400 -d data-LBp01ef1 -o props-LBp01ef1  +
-   ​seriesprops -T0 0 -T1 400 -d data-LBp01ef1 -o props-LBm01ef1  +
-\\ +
-\\ +
-8. Make movies of the two flows with ''​movieframes''​ +
-\\ +
-\\ +
-   ​movieframes -T0 0 -T1 100 -d data-LBp01ef1 -o frames-LBp01ef1 +
-   ​movieframes -T0 0 -T1 100 -d data-LBm01ef1 -o frames-LBm01ef1+
gtspring2009/schedule/chflow1.1232937135.txt.gz · Last modified: 2009/01/25 18:32 by dspieker

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