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gtspring2009:schedule:chflow1 [2009/01/20 06:49]
gibson created 		gtspring2009:schedule:chflow1 [2010/02/02 07:55] (current)
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    * > 10^5-d state space, > 1 MB for each data point    * > 10^5-d state space, > 1 MB for each data point
    * Integration is computationally expensive    * Integration is computationally expensive
 +\\ 
 +\\
  //​this changes your workflow...// ​  //​this changes your workflow...// ​
    * integrate a flow and save velocity field to disk at regular intervals    * integrate a flow and save velocity field to disk at regular intervals
    * read saved data from disk for visualization,​ statistics, etc.    * read saved data from disk for visualization,​ statistics, etc.
    * run jobs on number crunchers (PACE), transfer files via scp, ...    * run jobs on number crunchers (PACE), transfer files via scp, ...
 +\\ 
 +\\
 //...and changes your analytic framework// //...and changes your analytic framework//
    * can't represent du/dt = F(u) simply    * can't represent du/dt = F(u) simply
-   * can't compute a 10^5 x 10^5 Jacobian matrix ​ +   * can't compute a 10^5 x 10^5 Jacobian matrix (even with sparse structure) 
-   ​* ​(even with sparse structure) +   * hard to choose projections for state-space portraits 
- +\\ 
 +\\
 All this makes numerical analysis of fluid dynamics a hassle, compared to low-dimensional All this makes numerical analysis of fluid dynamics a hassle, compared to low-dimensional
 ODE systems. ​ ODE systems. ​
Line 34: Line 36:
 and algorithms and giving them simple, flexible, high-level interfaces: and algorithms and giving them simple, flexible, high-level interfaces:
    * in C++ classes, for writing your own fluids codes    * in C++ classes, for writing your own fluids codes
-   * in predefined utility programs, for  +   * in predefined utility programs, for common calculations 
 +\\ 
 +\\
 We will discuss programming in channelflow another day. We will discuss programming in channelflow another day.
  
 Today is about using predefined channelflow utility programs to do calculations. Today is about using predefined channelflow utility programs to do calculations.
  
 +The utilities plus Matlab form a crude interactive system for CFD. 
  
 ===== Important concepts ===== ===== Important concepts =====
- 
- 
 ==== FlowField ==== ==== FlowField ====
  
Line 65: Line 67:
 gridpoint, there'​s a utility for conversion (field2ascii). gridpoint, there'​s a utility for conversion (field2ascii).
  
-==== Channelflow ​utilities ​==== +In channelflow ​utilities, velocity fields u(x,t) are **differences ​from the laminar ​flow**
- +
-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.  +
- +
-===== 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>​ <​latex>​
-u_{\pm}(x,t) = f^t(u_{LB} \pm v_{LB}), t \in [0, \infty]+{\bf u}_{total}({\bx x}, t) = {\bf u}({\bx x}, t) + y {\bf e}_x
 </​latex>​ </​latex>​
  
-using several channelflow utilities:  +so that they have Dirichlet boundary conditions and form a vector space. The Matlab visualization 
- +scripts add the laminar flow back on by default.
-  * ''​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 +
-    +
- +
-=== addfields ===  +
- +
-Add a small pertubation along the unstable manifold +
- +
-  addfields 1 uLB  0.01 uLBef1 ​ uLBp01ef1 +
-  addfields 1 uLB -0.01 uLBef1 ​ uLBm01ef1 +
- +
- +
-=== couette ===  +
- +
-Integrate the perturbations  +
- +
-   ​couette -T0 0 -T1 400 -o data-uLBp01ef1 uLBp01ef1 +
-   ​couette -T0 0 -T1 400 -o data-uLBm01ef1 uLBm01ef1 +
- +
- +
-=== seriesprops ===  +
- +
-Produce input vs dissipation curves for perturbations +
- +
-   ​seriesprops -T0 0 -T1 400 -d data-uLBp01ef1 -o ivd-uLBp01ef1  +
-   ​seriesprops -T0 0 -T1 400 -d data-uLBp01ef1 -o ivd-uLBm01ef1 ​+
  
 +**Note: I moved the rest of this class tutorial into the ** [[docs:​tutorial|channelflow tutorial]]. //John Gibson 2009-01-29//​
gtspring2009/schedule/chflow1.1232462952.txt.gz · Last modified: 2009/01/20 06:49 by gibson

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