fluidsim.solvers.ns2d.solver

NS2D solver (`fluidsim.solvers.ns2d.solver`)

This module provides two classes defining the pseudo-spectral solver 2D incompressible Navier-Stokes equations (ns2d).

class fluidsim.solvers.ns2d.solver.InfoSolverNS2D(only_root=False, **kargs)[source]

Bases: InfoSolverPseudoSpectral

Contain the information on the solver ns2d.

_init_root()[source]

Init. self by writing the information on the solver.

The function InfoSolverPseudoSpectral._init_root is called. We keep two classes listed by this function:

The other first-level classes for this solver are:

class fluidsim.solvers.ns2d.solver.Simul(params)[source]

Bases: SimulBasePseudoSpectral

Pseudo-spectral solver 2D incompressible Navier-Stokes equations.

InfoSolver: alias of InfoSolverNS2D

static _complete_params_with_default(params)[source]: Complete the params container (static method).

tendencies_nonlin(state_spect=None, old=None)[source]

Compute the nonlinear tendencies.

Parameters:

state_spectfluidsim.base.setofvariables.SetOfVariables

optional

Array containing the state, i.e. the vorticity, in Fourier space. If state_spect, the variables vorticity and the velocity are computed from it, otherwise, they are taken from the global state of the simulation, self.state.

These two possibilities are used during the Runge-Kutta time-stepping.

Returns:

tendencies_fftfluidsim.base.setofvariables.SetOfVariables: An array containing the tendencies for the vorticity.

Notes

The 2D Navier-Stokes equation can be written as:

\[\partial_t \hat\zeta = \hat N(\zeta) - \sigma(k) \hat \zeta,\]

This function compute the nonlinear term (“tendencies”) \(N(\zeta) = - \mathbf{u}\cdot \mathbf{\nabla} \zeta\).

Default parameters

<params NEW_DIR_RESULTS="True" ONLY_COARSE_OPER="False" beta="0.0" nu_2="0.0"
        nu_4="0.0" nu_8="0.0" nu_m4="0.0" short_name_type_run="">
  <oper Lx="8" Ly="8" NO_KY0="False" NO_SHEAR_MODES="False"
        coef_dealiasing="0.6666666666666666" nx="48" ny="48"
        truncation_shape="cubic" type_fft="default"/>  

  <time_stepping USE_CFL="True" USE_T_END="True" cfl_coef="None" deltat0="0.2"
                 deltat_max="0.2" it_end="10" max_elapsed="None" t_end="10.0"
                 type_time_scheme="RK4">
    <phaseshift_random nb_pairs="1" nb_steps_compute_new_pair="None"/>  

  </time_stepping>

  <init_fields available_types="['from_file', 'from_simul', 'in_script',
               'constant', 'noise', 'jet', 'dipole']" modif_after_init="False"
               type="constant">
    <from_file path=""/>  

    <constant value="1.0"/>  

    <noise length="0.0" velo_max="1.0"/>  

  </init_fields>

  <forcing available_types="['in_script', 'in_script_coarse', 'pseudo_spectral',
           'proportional', 'tcrandom', 'tcrandom_anisotropic']" enable="False"
           forcing_rate="1.0" key_forced="None" nkmax_forcing="5"
           nkmin_forcing="4" type="">
    <milestone nx_max="None">
      <objects diameter="1.0" number="2" type="cylinders"
               width_boundary_layers="0.1"/>  

      <movement type="uniform">
        <uniform speed="1.0"/>  

        <sinusoidal length="1.0" period="1.0"/>  

        <periodic_uniform length="1.0" length_acc="1.0" speed="1.0"/>  

      </movement>

    </milestone>

    <normalized constant_rate_of="None" type="2nd_degree_eq"
                which_root="minabs"/>  

    <random only_positive="False"/>  

    <tcrandom time_correlation="based_on_forcing_rate"/>  

    <tcrandom_anisotropic angle="45°" delta_angle="None"
                          kz_negative_enable="False"/>  

  </forcing>

  <output HAS_TO_SAVE="True" ONLINE_PLOT_OK="True" period_refresh_plots="1"
          sub_directory="">
    <periods_save increments="0" phys_fields="0" spatial_means="0"
                  spatiotemporal_spectra="0" spect_energy_budg="0" spectra="0"
                  spectra_multidim="0" temporal_spectra="0"/>  

    <periods_print print_stdout="1.0"/>  

    <periods_plot phys_fields="0"/>  

    <phys_fields field_to_plot="rot" file_with_it="False"/>  

    <spectra HAS_TO_PLOT_SAVED="False"/>  

    <spectra_multidim HAS_TO_PLOT_SAVED="False"/>  

    <spatial_means HAS_TO_PLOT_SAVED="False"/>  

    <spect_energy_budg HAS_TO_PLOT_SAVED="False"/>  

    <increments HAS_TO_PLOT_SAVED="False"/>  

    <temporal_spectra SAVE_AS_FLOAT32="True" file_max_size="10.0"
                      probes_deltax="0.1" probes_deltay="0.1"
                      probes_region="None"/>  

    <spatiotemporal_spectra SAVE_AS_COMPLEX64="True" file_max_size="10.0"
                            probes_region="None"/>  

  </output>

  <preprocess enable="False" forcing_const="1.0" forcing_scale="unity"
              init_field_const="1.0" init_field_scale="unity"
              viscosity_const="1.0" viscosity_scale="enstrophy_forcing"
              viscosity_type="laplacian"/>  

</params>

Documentation for params

short_name_type_run: str

A short name of the simulation used to create the directory name.

NEW_DIR_RESULTS: bool

To be used only when loading a simulation. If True (default), a new directory is created to contain the results of the simulation. If False, the results of the simulation are appended in the old directory.

ONLY_COARSE_OPER: bool

To be used only when loading a simulation. If True (not default), the operator is created with a very small resolution. It is very fast but then it can not be used to process data.

nu_2: float (default = 0.)

Viscosity coefficient. Used in particular in the method fluidsim.base.solvers.pseudo_spect.SimulBasePseudoSpectral.compute_freq_diss()).

nu_8: float

Hyper-viscous coefficient of order 8. Also used in the method compute_freq_diss.

nu_4: float

Hyper-viscous coefficient of order 4.

nu_m4: float

Hypo-viscous coefficient of order -4. Hypo-viscosity affect more the large scales.

Documentation for params.oper

Documentation for params.time_stepping

See fluidsim.base.time_stepping.base.

USE_T_END: bool (default True)

If True, time step until t > t_end. If False, time step until it >= it_end.

t_end: float

See documentation USE_T_END.

it_end: int

If USE_T_END is False, number of time steps.

USE_CFL: bool (default False)

If True, use an adaptive time step computed in particular with a Courant-Friedrichs-Lewy (CFL) condition.

type_time_scheme: str (default “RK4”)

Type of time scheme. Can be in (“RK2”, “RK4”).

deltat0: float (default 0.2)

If USE_CFL is False, value of the time step.

deltat_max: float (default 0.2)

Maximum value of the time step (useful when USE_CFL is True).

cfl_coef: float (default None)

If not None, clf_coef used in the CFL condition. If None, the value is choosen taking into account the time scheme.

max_elapsed: number or str (default None)

If not None, the computation stops when the elapsed time becomes larger than max_elapsed. Can be a number (in seconds) or a string (formated as “%H:%M:%S”).

Documentation for params.time_stepping.phaseshift_random

Documentation for params.init_fields

See fluidsim.base.init_fields.

type: str (default constant)

Name of the initialization method.

available_types: list

Actually not a parameter; just a hint to set type.

modif_after_init: bool (default False)

Used internally when reloading some simulations.

Documentation for params.init_fields.from_file

path: str

Documentation for params.init_fields.constant

value: float (default 1.)

Documentation for params.init_fields.noise

velo_max: float (default 1.)

Maximum velocity.

length: float (default 0.)

The smallest (cutoff) scale in the noise.

Documentation for params.forcing

How the forcing is normalized

Documentation for params.forcing.milestone

Documentation for params.forcing.milestone.objects

Documentation for params.forcing.milestone.movement

Documentation for params.forcing.milestone.movement.uniform

Documentation for params.forcing.milestone.movement.sinusoidal

Documentation for params.forcing.milestone.movement.periodic_uniform

Documentation for params.forcing.normalized

Documentation for params.forcing.random

Documentation for params.forcing.tcrandom

Documentation for params.forcing.tcrandom_anisotropic

See fluidsim.base.forcing.anisotropic.

angle: float or str

Angle between the wavevector and the horizontal characterising the forcing region.

delta_angle: float or None

Control the shape of the forcing region in k-space. If None, (khmin, khmax, kvmin, kvmax) are computed from the angle, params.forcing.nkmin_forcing and params.forcing.nkmax_forcing.

kz_negative_enable: bool

If True, modes with negative kz are also forced.

Documentation for params.output

See fluidsim.output.base

ONLINE_PLOT_OK: bool (default: True)

If True, the online plots are enabled.

period_refresh_plots: float (default: 1)

Period of refreshment of the online plots.

HAS_TO_SAVE: bool (default: True)

If False, nothing new is saved in the directory of the simulation.

sub_directory: str (default: “”)

A name of a subdirectory where the directory of the simulation is saved.

Documentation for params.output.periods_save

Periods (float, in equation time) to set when the specific outputs are saved.

Documentation for params.output.periods_print

Periods (float, in equation time) to set when the printing specific outputs are called.

Documentation for params.output.periods_plot

Periods (float, in equation time) to set when the plots of the specific outputs are called.

Documentation for params.output.phys_fields

Documentation for params.output.spectra

Documentation for params.output.spectra_multidim

Documentation for params.output.spatial_means

Documentation for params.output.spect_energy_budg

Documentation for params.output.increments

Documentation for params.output.temporal_spectra

probes_deltax, probes_deltay and probes_deltaz: float (default: 0.1)

Probes spacing in the x, y and z directions (in params.oper.Li unit).

probes_region: tuple (default:None)

Boundaries of the region in the simulation domain were probes are set.

probes_region = (xmin, xmax, ymin, ymax, zmin, zmax), in params.oper.Lx unit.

If None, set to the whole simulation domain.

file_max_size: float (default: 10.0)

Maximum size of one time series file, in megabytes.

SAVE_AS_FLOAT32: bool (default: True)

If set to False, probes data is saved as float64.

Warning : saving as float64 reduces digital noise at high frequencies, but double the size of the output!

Documentation for params.output.spatiotemporal_spectra

probes_region: int tuple (default:None)

Boundaries of the region to record in the spectral domain.

probes_region = (ikxmax, ikymax, ikzmax), in nondimensional units (mode indices).

The resulting ranges for each wavevectors are :

ikx in [0 , ikxmax]

iky in [-ikymax+1 , ikymax]

ikz in [-ikzmax+1 , ikzmax]

If None, set all ikmax = 4.

file_max_size: float (default: 10.0)

Maximum size of one time series file, in megabytes.

SAVE_AS_COMPLEX64: bool (default: True)

If set to False, probes data is saved as complex128.

Warning : saving as complex128 reduces digital noise at high frequency, but doubles the size of the output!

Documentation for params.preprocess

Functions

compute_Frot(ux, uy, px_rot, py_rot[, beta])

Classes

`InfoSolverNS2D`([only_root])	Contain the information on the solver ns2d.
`Simul`(params)	Pseudo-spectral solver 2D incompressible Navier-Stokes equations.