# -*- coding: utf-8 -*-
"""Boussinesq NS3D solver (:mod:`fluidsim.solvers.ns3d.bouss.solver`)
=====================================================================
.. autoclass:: InfoSolverNS3DBouss
:members:
:private-members:
.. autoclass:: Simul
:members:
:private-members:
"""
from fluidfft.fft3d.operators import vector_product
from fluidsim.base.setofvariables import SetOfVariables
from ..strat.solver import InfoSolverNS3DStrat, Simul as SimulStrat
[docs]
class InfoSolverNS3DBouss(InfoSolverNS3DStrat):
[docs]
def _init_root(self):
super()._init_root()
package = "fluidsim.solvers.ns3d.bouss"
self.module_name = package + ".solver"
self.class_name = "Simul"
self.short_name = "ns3d.bouss"
# classes = self.classes
# classes.State.module_name = package + '.state'
# classes.State.class_name = 'StateNS3DStrat'
# classes.InitFields.module_name = package + '.init_fields'
# classes.InitFields.class_name = 'InitFieldsNS3D'
# classes.Output.module_name = package + '.output'
# classes.Output.class_name = 'Output'
# classes.Forcing.module_name = package + '.forcing'
# classes.Forcing.class_name = 'ForcingNS3D'
[docs]
class Simul(SimulStrat):
r"""Pseudo-spectral solver 3D incompressible Navier-Stokes equations.
Notes
-----
.. |p| mathmacro:: \partial
.. |vv| mathmacro:: \textbf{v}
.. |kk| mathmacro:: \textbf{k}
.. |ek| mathmacro:: \hat{\textbf{e}}_\textbf{k}
.. |bnabla| mathmacro:: \boldsymbol{\nabla}
This class is dedicated to solve with a pseudo-spectral method the
incompressible Navier-Stokes equations (possibly with hyper-viscosity):
.. math::
\p_t \vv + \vv \cdot \bnabla \vv =
- \bnabla p - \nu_\alpha (-\Delta)^\alpha \vv,
where :math:`\vv` is the non-divergent velocity (:math:`\bnabla
\cdot \vv = 0`), :math:`p` is the pressure, :math:`\Delta` is the
3D Laplacian operator.
In Fourier space, these equations can be written as:
.. math::
\p_t \hat v = N(v) + L \hat v,
where
.. math::
N(\vv) = -P_\perp \widehat{\bnabla \cdot \vv \vv},
.. math::
L = - \nu_\alpha |\kk|^{2\alpha},
with :math:`P_\perp = (1 - \ek \ek \cdot)` the operator projection on the
plane perpendicular to the wave number :math:`\kk`. Since the flow is
incompressible (:math:`\kk \cdot \vv = 0`), the effect of the pressure term
is taken into account with the operator :math:`P_\perp`.
"""
InfoSolver = InfoSolverNS3DBouss
[docs]
def tendencies_nonlin(self, state_spect=None, old=None):
oper = self.oper
ifft_as_arg = oper.ifft_as_arg
ifft_as_arg_destroy = oper.ifft_as_arg_destroy
fft_as_arg = oper.fft_as_arg
if state_spect is None:
spect_get_var = self.state.state_spect.get_var
else:
spect_get_var = state_spect.get_var
vx_fft = spect_get_var("vx_fft")
vy_fft = spect_get_var("vy_fft")
vz_fft = spect_get_var("vz_fft")
b_fft = spect_get_var("b_fft")
omegax_fft, omegay_fft, omegaz_fft = oper.rotfft_from_vecfft(
vx_fft, vy_fft, vz_fft
)
if self.params.f is not None:
self._modif_omegafft_with_f(omegax_fft, omegay_fft, omegaz_fft)
omegax = self.state.fields_tmp[3]
omegay = self.state.fields_tmp[4]
omegaz = self.state.fields_tmp[5]
ifft_as_arg_destroy(omegax_fft, omegax)
ifft_as_arg_destroy(omegay_fft, omegay)
ifft_as_arg_destroy(omegaz_fft, omegaz)
if state_spect is None:
vx = self.state.state_phys.get_var("vx")
vy = self.state.state_phys.get_var("vy")
vz = self.state.state_phys.get_var("vz")
else:
vx = self.state.fields_tmp[0]
vy = self.state.fields_tmp[1]
vz = self.state.fields_tmp[2]
ifft_as_arg(vx_fft, vx)
ifft_as_arg(vy_fft, vy)
ifft_as_arg(vz_fft, vz)
fx, fy, fz = vector_product(vx, vy, vz, omegax, omegay, omegaz)
if old is None:
tendencies_fft = SetOfVariables(
like=self.state.state_spect, info="tendencies_nonlin"
)
else:
tendencies_fft = old
fx_fft = tendencies_fft.get_var("vx_fft")
fy_fft = tendencies_fft.get_var("vy_fft")
fz_fft = tendencies_fft.get_var("vz_fft")
fft_as_arg(fx, fx_fft)
fft_as_arg(fy, fy_fft)
fft_as_arg(fz, fz_fft)
fz_fft += b_fft
if state_spect is None:
b = self.state.state_phys.get_var("b")
else:
b = self.state.fields_tmp[3]
ifft_as_arg(b_fft, b)
fb_fft = -oper.div_vb_fft_from_vb(vx, vy, vz, b)
tendencies_fft.set_var("b_fft", fb_fft)
if self.is_forcing_enabled:
tendencies_fft += self.forcing.get_forcing()
self.project_state_spect(tendencies_fft)
self.oper.dealiasing(tendencies_fft)
return tendencies_fft
if __name__ == "__main__":
import numpy as np
# import fluiddyn as fld
params = Simul.create_default_params()
params.short_name_type_run = "test"
n = 64
L = 10
params.oper.nx = n * 2
params.oper.ny = 32
params.oper.nz = 8
params.oper.Lx = L
params.oper.Ly = L
params.oper.Lz = L
# params.oper.type_fft = 'fluidfft.fft3d.mpi_with_fftwmpi3d'
# params.oper.type_fft = 'fluidfft.fft3d.with_pyfftw'
# params.oper.type_fft = 'fluidfft.fft3d.with_cufft'
# delta_x = params.oper.Lx / params.oper.nx
params.nu_8 = 2e-6
params.time_stepping.USE_T_END = True
params.time_stepping.t_end = 10.0
params.init_fields.type = "in_script"
# params.forcing.enable = False
# params.forcing.type = 'random'
# 'Proportional'
# params.forcing.type_normalize
params.output.periods_print.print_stdout = 0.00000000001
params.output.periods_save.phys_fields = 1.0
# params.output.periods_save.spectra = 0.5
# params.output.periods_save.spatial_means = 0.05
# params.output.periods_save.spect_energy_budg = 0.5
# params.output.periods_plot.phys_fields = 0.0
params.output.ONLINE_PLOT_OK = True
# params.output.spectra.HAS_TO_PLOT_SAVED = True
# params.output.spatial_means.HAS_TO_PLOT_SAVED = True
# params.output.spect_energy_budg.HAS_TO_PLOT_SAVED = True
# params.output.phys_fields.field_to_plot = 'rot'
sim = Simul(params)
# here we have to initialize the flow fields
variables = {
k: 1e-6 * sim.oper.create_arrayX_random() for k in ("vx", "vy", "vz")
}
X, Y, Z = sim.oper.get_XYZ_loc()
x0 = y0 = z0 = L / 2.0
R2 = (X - x0) ** 2 + (Y - y0) ** 2 + (Z - z0) ** 2
r0 = 0.5
b = -np.exp(-R2 / r0**2)
variables["b"] = b
sim.state.init_statephys_from(**variables)
sim.state.statespect_from_statephys()
sim.state.statephys_from_statespect()
# sim.output.phys_fields.plot()
sim.time_stepping.start()
# sim.output.phys_fields.plot()
# fld.show()