153 lines
5.9 KiB
Markdown
153 lines
5.9 KiB
Markdown
Nstrophy is a tool to solve the two-dimensional Navier-Stokes equation as well
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as Gallavotti's reversible Navier-Stokes equation and compare them.
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**Nstrophy is under active development**
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# Building
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Compile Nstrophy with
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```bash
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make
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```
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which will place a binary at `build/nstrophy`.
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The syntax for the execution of Nstrophy is
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```bash
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./build/nstrophy [-p parameters] [-s savefile] [-u u_outfile] [-t nthreads] <command>
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```
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* `parameters` is a list of parameters for the computation, see
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[Parameters](#parameters)
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* `savefile` is a file where the last step of the computation is saved in
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binary format so that the computation can be resumed after it has terminated,
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see
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[Interrupting and resuming the computation](#interrupting-and-resuming-the-computation).
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* `u_outfile` is a file to which the final u is written in plain text format,
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which can be used as an initial condition for a future computation.
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* `nthreads` is the number of threads used to compute Fast Fourier Transforms.
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Nstrophy is written in C. The Makefile uses the GNU C Compiler.
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Nstrophy depends on `fftw`: [https://fftw.org]
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# Commands
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The available commands are
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* `enstrophy`: to compute the enstrophy and various other observables. This
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command prints
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```step_index time average(alpha) average(energy) average(enstrophy) alpha energy enstrophy```
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where the averages are running averages over `print_freq`. In addition, if
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the algorithm has an adaptive step, an extra column is printed with `delta`.
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In addition, if alpha has a negative value (even in between `print_freq`
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intervals), a line is printed with the information.
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* `uk`: to compute the Fourier transform of the solution.
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* `quiet`: does not print anything, useful for debugging.
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# Parameters
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The parameters can be specified using the `-p` flag. The parameter string
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should be a `;` sperated list of `key=value` pairs. The possible keys are
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* `equation`: either `irreverisible` (default) or `reversible`.
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* `K` (int, default 16): cutoff in momentum space: -K<=k_i<=K
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* `K1` (int, default `K`): cutoff in momentum space for the x component:
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-K<=k_x<=K
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* `K2` (int, default `K`): cutoff in momentum space for the y component:
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-K<=k_y<=K
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* `N` (int, default smallest power of 2 that is larger than 3`K`): size of fft
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vectors: must be at least 3 times `K` to avoid aliasing.
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* `N1` (int, default `N`): same as `N` but only for x component.
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* `N2` (int, default `N`): same as `N` but only for y component.
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* `final_time` (double, default 100000): time at which to end the computation.
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Set to <0 to keep on going forever.
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* `nu` (double, default 0.00048828125): viscosity.
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* `delta` (double, default 0.0001220703125): step size.
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* `L` (double, default 2pi): size of box.
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* `print_freq` (double, default 1): only print when time crosses integer
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multiples of `print_freq`.
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* `starting_time` (double, default 0): starting time.
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* `driving`: either `zero` for no driving, `test` (default) for a testing
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driving force or `file:<filename>` or `file_txt:<filename>` to read the
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driving force from a file. When using `file:<filename>` the file should be
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binary, whereas with `file_txt:<filename>` it should be plaintext. The binary
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file format is `(double)(double)` for each entry of the driving force,
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excluding kx<0 and kx=0&&ky<=0. The plaintext file format is
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`kx ky real_part imag_part`.
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* `init`: either `random` for a random initialization, `gaussian` (default) for
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a Gaussian initial condition or `file:<filename>` or `file_txt:<filename>` to
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read the driving force from a file. When using `file:<filename>` the file
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should be binary, whereas with `file_txt:<filename>` it should be plaintext.
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The binary file format is `(double)(double)` for each entry of the driving
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force, excluding kx<0 and kx=0&&ky<=0. The plaintext file format is
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`kx ky real_part imag_part`.
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* `init_en` (double, default 1.54511597324389e+02): initial value of the energy if
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`equation=irreversible` or of the enstrophy if `equation=reversible`.
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* `random_seed` (int, default ): seed for random initialization.
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* `algorithm`: fixed step methods: `RK4` for Runge-Kutta 4, `RK2` for
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Runge-Kutta 2.
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adaptive step methods: `RKF45` for Runge-Kutta-Fehlberg (order
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4), `RKDP54` for Runge-Kutta-Dormand-Prince (order 5), `RKBS32` for
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Runge-Kutta-Bogacki-Shampine (order 3).
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* `adaptive_tolerance` (double, default 1e-11): when using an adaptive step
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method, this is the maximal allowed relative error.
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* `adaptive_factor` (double, default 0.9): when using the RKF45 method, the
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step gets adjusted by `factor*delta*(tolerance/error)^(1/5)`.
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* `max_delta` (double, default 1e-2): when using the adaptive step, do not
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exceet `delta_max`.
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* `adaptive_cost`: cost function to use to estimate the error of the adaptive
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method: `L1` (default) for the normalized L1 norm, `k3` for the normalized L1
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norm of f_k/|k|^3, `k32` for the normalized L1 norm, `enstrophy` for the
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enstrophy, `alpha` for alpha.
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* `keep_en_cst` (0 or 1, default 0): impose that the enstrophy is constant at
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each step (only really useful for the reversible equation).
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* `print_alpha` (0 or 1, default 0): if this is set to 1, then whenever alpha
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is negative, its value is printed as a comment.
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# Interrupting and resuming the computation
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The computation can be interrupted by sending Nstrophy the `SIGINT` signal
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(e.g. by pressing `Ctrl-C`.) When Nstrophy receives the `SIGINT` signal, it
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finishes its current step and writes the value of uk, either to `savefile` if
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such a file was specified on the command line (using the `-s` flag), or to
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`stderr`. In addition, when a `savefile` is specified it writes the command
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that needs to be used to resume the computation (which essentially just sets
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the appropriate `starting_time` and `init:file:<savefile>` parameters. The data
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written to the `savefile` is binary.
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# License
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Nstrophy is released under the Apache 2.0 license.
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Copyright 2017-2024 Ian Jauslin
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