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====== Channelflow Tutorial ====== | ====== Channelflow Tutorial ====== | ||
- | |||
- | ===== Intro ===== | ||
So you've installed channelflow. Now what? Well, computational fluid | So you've installed channelflow. Now what? Well, computational fluid | ||
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of my own research. Probably the best way to get started with | of my own research. Probably the best way to get started with | ||
channelflow is to step through a few examples of run-of-the-mill | channelflow is to step through a few examples of run-of-the-mill | ||
- | calculations using these utilities. If you want to get right to these | + | calculations using these utilities. |
- | examples, skip to Section 3. | + | |
- | + | ||
- | + | ||
- | ===== Overview of channelflow utility programs ===== | + | |
- | + | ||
- | Here's a list of current channelflow utilities. The first three | + | |
- | are taken out of alphabetical order because they're featured in | + | |
- | Section 3, Example Calculations. | + | |
- | + | ||
- | ^ program name ^ purpose ^ | + | |
- | | randomfield | build a random initial velocity field, save to disk | | + | |
- | | couette | integrate an initial condition, save results to disk | | + | |
- | | fieldprops | print out norms, symmetries, geometrical data of a stored field | | + | |
- | | makemovie | extract slices of fields in order to make a movie | | + | |
- | | addfields | compute sum a_n u_n and store result to disk | | + | |
- | | arnoldi | compute the eigenvalues and eigenfunctions of eqbs and orbits | | + | |
- | | ascii2field | convert a file of ASCII data to a channelflow FlowField | | + | |
- | | changegrid | change the discretization or box size of a field | | + | |
- | | field2ascii | convert a channelflow FlowField to a file of ASCII data | | + | |
- | | fieldplots | extract a number of 2D slices of the 3D field, good for plots | | + | |
- | | findorbit | compute an equilibrium or periodic orbit of plane Couette | | + | |
- | | L2Dist | compute the L2 distance between two fields | | + | |
- | | L2IP | compute the L2 inner product | | + | |
- | | makebasis | construct an orthonormal basis from a set of fields | | + | |
- | | makeheatmode | construct a field that decays in time according to Laplace eqn | | + | |
- | | makestokesmode | construct a stokes eigenfunction of laminar equilibrium | | + | |
- | | perturbfield | add random perturbations to a given field | | + | |
- | | projectfields | project a set of fields onto a given basis | | + | |
- | | projectseries | project a sequence of fields onto a given basis | | + | |
- | | seriesprops | compute statistics on a sequence of data | | + | |
- | | symmetrize | find the phase shift of a field that optimizes symmetries | | + | |
- | + | ||
- | 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 | + | Please refer to [[:docs#utilities|Utilities]] and [[docs:utils:options|Utility Options]] |
+ | for a detailed guide of individual utilities and their options. You can also run any | ||
+ | utility with a ''-h'' or ''--help'' option to get a brief description of the | ||
+ | utility's purpose and options, e.g | ||
- | and a list of its command-line options and arguments. Channelflow | + | <code> |
- | utilities are invoked at the command line with syntax like | + | couette --help |
+ | </code> | ||
- | utility -opt1 value -opt2 value -flag1 arg3 arg2 arg1 | ||
- | or concretely | + | ====== Example Calculations ====== |
+ | ===== Making a movie ===== | ||
- | couette -T0 0 -T1 -vdt -dt 0.02 -ts sbdf4 u0.ff | + | ===1. Generate an initial condition and examine its properties === |
- | + | gibson@akbar$ randomfield -Nx 48 -Ny 33 -Nz 48 -lx 2 -lz 1 -m 0.20 u0.ff | |
- | "Options" (e.g. -opt1 value) are used to reset default values | + | |
- | of parameters. For options, the first two columns in the built-in | + | |
- | help give the short and long form of the option (e.g. -ts and | + | |
- | --timestepping), the third column indicates the type of parameter | + | |
- | expected (e.g. real, int, bool, string), and the fourth gives the | + | |
- | the default value. For example, "couette -dt 0.02 -ts cnab2" sets | + | |
- | the time stepping method to 2nd order Crank-Nicolson Adams-Bashforth | + | |
- | with dt=0.02. | + | |
- | + | ||
- | "Flags" simply turn on boolean options that would otherwise be set | + | |
- | to false. For example, calling "couette -vdt" turns on variable-dt | + | |
- | timestepping, which adjusts dt at fixed intervals to keep the CFL | + | |
- | number within bounds. For flags the third and fourth columns of | + | |
- | built-in help are left blank. | + | |
- | + | ||
- | "Arguments" always come after all options and flags. Arguments usually | + | |
- | specify the filenames of binary velocity fields that the utility will | + | |
- | load and operate on. Most channelflow programs have one required | + | |
- | argument (e.g. "couette u0.ff") some two (e.g. "L2Dist u0.ff u2.ff"). | + | |
- | Others take a variable number of arguments (e.g. makebasis u0 u1 u2"). | + | |
- | Unfortunately it's difficult to document variable-number arguments | + | |
- | properly in the four-column option system, so variable-number arguments | + | |
- | are usually documented with a "usage: line right after the description | + | |
- | of the utility's purpose. | + | |
- | + | ||
- | So, as you read work through the Example Calculations, you can run the | + | |
- | suggested command with a --help option to clarify what the options are | + | |
- | doing and what other options are possible. | + | |
- | + | ||
- | + | ||
- | ===== Example Calculations ===== | + | |
- | ==== Making a movie ==== | + | |
- | + | ||
- | === 1. Generate an initial condition and examine its properties === | + | |
- | + | ||
- | gibson@akbar$ randomfield -Nx 48 -Ny 35 -Nz 48 -lx 0.875 -lz 0.6 -m 0.20 u0.ff | + | |
This command generates a no-slip, divergence-free velocity field with | This command generates a no-slip, divergence-free velocity field with | ||
- | random spectral coefficients on a 48 x 35 x 48 grid, on [0, 2pi] x | + | random spectral coefficients on a 48 x 33 x 48 grid, on [0, 2pi] x |
[-1, 1] x [0, pi], with magnitude 1/V \integral_V |u|^2 dx = 0.2. The | [-1, 1] x [0, pi], with magnitude 1/V \integral_V |u|^2 dx = 0.2. The | ||
field is a perturbation from the laminar flow --by default, velocity | field is a perturbation from the laminar flow --by default, velocity | ||
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Adjust the bitrate to balance filesize and video quality. | Adjust the bitrate to balance filesize and video quality. | ||
- | ==== Computing a 1d unstable manifold ==== | + | ===== Computing a 1d unstable manifold ===== |
The Nagata (1990) "lower-branch" equilibrium has a one-dimensional unstable manifold. | The Nagata (1990) "lower-branch" equilibrium has a one-dimensional unstable manifold. | ||
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* ''projectseries'' | * ''projectseries'' | ||
- | === Download the Nagata lower-branch solution === | + | === 1. Download the Nagata lower-branch solution === |
...from the [[http://www.channelflow.org/database|channelflow database]]. ''LB'' stands for 'lower-branch'. | ...from the [[http://www.channelflow.org/database|channelflow database]]. ''LB'' stands for 'lower-branch'. | ||
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wget http://channelflow.org/database/a1.14_g2.5_Re400/LB.ff | wget http://channelflow.org/database/a1.14_g2.5_Re400/LB.ff | ||
- | === Examine the solution's properties === | + | === 2. Examine the solution's properties === |
The ''fieldprops'' utility will print out basic information about the field. For example, | The ''fieldprops'' utility will print out basic information about the field. For example, | ||
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if you leave it off. | if you leave it off. | ||
- | === Plot the solution === | + | === 3. Plot the solution === |
Visualization of fluid velocity fields is an art in itself. Channelflow provides a | Visualization of fluid velocity fields is an art in itself. Channelflow provides a | ||
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- | === Compute the eigenfunctions === | + | === 4. Compute the eigenfunctions === |
The Nagata lower-branch solution is an equilibrium of plane Couette dynamics. You can | The Nagata lower-branch solution is an equilibrium of plane Couette dynamics. You can | ||
compute the eigenvalues and eigenfunctions of the linearized dynamics about the equilbrium | compute the eigenvalues and eigenfunctions of the linearized dynamics about the equilbrium | ||
- | with the ''arnoldi'' utility. (Will write documentation on Arnolid iteration later). | + | with the ''arnoldi'' utility. (Will write documentation on Arnoldi iteration later). |
arnoldi --flow LB.ff | arnoldi --flow LB.ff | ||
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- | === Perturb along the unstable manifold === | + | === 5. Perturb along the unstable manifold === |
The Nagata lower branch has a single unstable eigenvalue, so its unstable manifold is 1d | The Nagata lower branch has a single unstable eigenvalue, so its unstable manifold is 1d | ||
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- | === Integrate the perturbations === | + | === 6. Integrate the perturbations === |
couette -T0 0 -T1 400 -o data-LBp01 LBp01ef1 | couette -T0 0 -T1 400 -o data-LBp01 LBp01ef1 | ||
- | couette -T1 0 -T1 400 -o data-LBm01 LBm01ef1 | + | couette -T0 0 -T1 400 -o data-LBm01 LBm01ef1 |
- | === Produce input vs dissipation curves === | + | === 7. Produce input vs dissipation curves === |
The ''seriesprops'' utility computes a few quantities like energy dissipation D and | The ''seriesprops'' utility computes a few quantities like energy dissipation D and | ||
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- | === Make movies === | + | === 8. Make movies === |
movieframes -T0 0 -T1 100 -d data-LBp01ef1 -o frames-LBp01ef1 | movieframes -T0 0 -T1 100 -d data-LBp01ef1 -o frames-LBp01ef1 | ||
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From here you can adapt the [[#make_a_movie_from_extracted_data|movie-making instructions]] from above. | From here you can adapt the [[#make_a_movie_from_extracted_data|movie-making instructions]] from above. | ||
- | ==== Project movie data onto state-space coordinates ==== | + | ===== Project movie data onto state-space coordinates ===== |
It can be useful to look at the temporal evolution of a fluid as | It can be useful to look at the temporal evolution of a fluid as | ||
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equilibria under the symmetries of plane Couette flow. In simple | equilibria under the symmetries of plane Couette flow. In simple | ||
language, we take linear combinations of equilibria and their | language, we take linear combinations of equilibria and their | ||
- | translations in x,z to form orthonormal basis sets. | + | translations in x,z to form orthonormal basis sets. For a more |
+ | detailed description of the logic and mathematics of this approach, | ||
+ | see [[:references|Gibson et al (2007) JFM 611]]. Here we will just | ||
+ | outline how the computation is done using channelflow. | ||
- | === Make a low-d basis === | + | === 1. Make a low-d basis === |
+ | |||
+ | Make a subdirectory and descend into it, so that the following steps | ||
+ | don't pollute the current directory with a bunch of extraneous files | ||
+ | |||
+ | mkdir basis-UBtrans | ||
+ | cd basis-UBtrans | ||
Download an equilibrium solution of plane Couette flow from the | Download an equilibrium solution of plane Couette flow from the | ||
channelflow website, one that is compatible in geometry and | channelflow website, one that is compatible in geometry and | ||
- | discretization. | + | discretization. For example, you can get the Nagata upper-branch |
+ | equilibrium (UB) with the Unix "wget" utility. | ||
+ | |||
+ | wget http://www.channelflow.org/database/a1.14_g2.5_Re400/UB.ff | ||
+ | |||
+ | Compute the half-cell translations of UB in x, in z, and in x,z with | ||
+ | the channelflow [[:docs:utils:symmetryop]] utility: | ||
+ | |||
+ | symmetryop -ax 0.5 UB UBx | ||
+ | symmetryop -az 0.5 UB UBz | ||
+ | symmetryop -ax 0.5 -az 0.5 UB UBxz | ||
+ | |||
+ | Briefly, symmetryop constructs a symmetry σ parameterized by the options, | ||
+ | applies it to the first FlowField argument, and saves the result to the | ||
+ | second FlowField argument, according to the symmetry parameterization described | ||
+ | in [[:docs:math:symmetry]]. Let if τ<sub>x</sub> be translation by Lx/2, etc. | ||
+ | Then the above lines compute τ<sub>x</sub> UB, τ<sub>z</sub>, and | ||
+ | τ<sub>xz</sub> respectively. | ||
+ | |||
+ | Now construct the following orthogonal linear combinations of the above fields | ||
+ | |||
+ | <latex> $ \begin{align*} | ||
+ | UB_{pppp} = UB + \tau_x UB + \tau_z UB + \tau_{xz} UB \\ | ||
+ | UB_{ppmm} = UB + \tau_x UB - \tau_z UB - \tau_{xz} UB \\ | ||
+ | UB_{pmpm} = UB - \tau_x UB + \tau_z UB - \tau_{xz} UB \\ | ||
+ | UB_{pmmp} = UB - \tau_x UB - \tau_z UB + \tau_{xz} UB | ||
+ | \end{align*} $ </latex> | ||
+ | |||
+ | with the channelflow [[:docs:utils:addfields]] utility: | ||
+ | |||
+ | addfields 1 UB 1 UBx 1 UBz 1 UBxz UBpppp | ||
+ | addfields 1 UB 1 UBx -1 UBz -1 UBxz UBppmm | ||
+ | addfields 1 UB -1 UBx 1 UBz -1 UBxz UBpmpm | ||
+ | addfields 1 UB -1 UBx -1 UBz 1 UBxz UBpmmp | ||
+ | |||
+ | Finally, use the channelflow [[:docs:utils:makebasis]] utility to | ||
+ | apply Gram-Schmidt orthogonalization on those fields and form an | ||
+ | orthonormal basis set: | ||
+ | |||
+ | makebasis UBpppp UBppmm UBpmpm UBpmmp | ||
+ | |||
+ | The output of "makebasis" will be four orthonormal basis elements e0.ff, e1.ff, | ||
+ | e2.ff, and e3.ff saved to disk. In this case the input fields are already orthogonal | ||
+ | and all "makebasis" does is normalize. | ||
+ | |||
+ | Now pop out of the basis-UBtrans subdirectory | ||
+ | |||
+ | cd .. | ||
+ | |||
+ | |||
+ | |||
+ | === 2. Project a series of fields onto the basis === | ||
+ | |||
+ | Ok. Suppose you have a series of velocity fields u0.ff, u1.ff, etc for t=0,1,2,...1000 | ||
+ | in a data/ directory and a set of basis elements e0.ff, e1.ff, e2.ff, e3.ff in a | ||
+ | basis-UBtrans/ directory. To project the fields onto the basis, run | ||
+ | |||
+ | projectseries -T0 0 -T1 1000 -d data -b basis-UBtrans -Nb 4 -o a.asc | ||
+ | |||
+ | That will produce an ASCII file a.asc with 4 columns and 1001 rows. The t-th row and jth | ||
+ | column is the value of (u(t), ej), where ( , ) signifies the L2 inner product | ||
+ | |||
+ | <latex> | ||
+ | (f,g) = 1/V \int_V f \cdot g dx dy dz | ||
+ | </latex> | ||
- | (to be continued...) | + | |
- | + | |