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VP1D4f_modules.py
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VP1D4f_modules.py
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#
# BSD 2-Clause License
#
# Copyright (c) 2021, Cristel Chandre
# All rights reserved.
#
# Redistribution and use in source and binary forms, with or without
# modification, are permitted provided that the following conditions are met:
#
# 1. Redistributions of source code must retain the above copyright notice, this
# list of conditions and the following disclaimer.
#
# 2. Redistributions in binary form must reproduce the above copyright notice,
# this list of conditions and the following disclaimer in the documentation
# and/or other materials provided with the distribution.
#
# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
# AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
# IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
# DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
# FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
# DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
# SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
# CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
# OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
# OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
import numpy as xp
from scipy.integrate import simpson, solve_ivp
from scipy.optimize import root
from tqdm import trange
from scipy.io import savemat
import time
from datetime import date
import matplotlib.pyplot as plt
import warnings
warnings.filterwarnings("ignore")
def integrate(case):
timestr = time.strftime("%Y%m%d_%H%M")
state_k = case.f.copy()
moments = case.compute_moments(state_k, 3)
moments[xp.abs(moments) <= case.precision] = 0
state_f = moments[:4, :].reshape(4*case.Nx).copy()
compute_G = lambda G: case.compute_S0(G) - state_f[2*case.Nx:]
sol = root(compute_G, case.compute_G0(state_f[2*case.Nx:]), tol=case.precision, method='krylov')
if ('Compute' in case.Fluid) and (not sol.success):
print('\033[31m Error: a correct determination for G2 and G3 was not found \033[00m')
print('\033[31m -> fluid computation is skipped \033[00m')
case.Fluid = []
else:
state_f[2*case.Nx:] = sol.x
state_f[xp.abs(state_f) <= case.precision] = 0
E_f = case.E(state_f[:case.Nx])
H0_f = case.energy_fluid(state_f, E_f)
C0_f = case.casimirs_fluid(state_f)
E_k = case.E(moments[0, :])
H0_k = case.energy_kinetic(state_k, E_k)
C0_k = case.casimirs_kinetic(state_k, case.n_casimirs)
if 'Plot' in case.Fluid:
dict_fluid = {'\\rho': moments[0, :],
'P': moments[0, :]**3 * moments[2, :],
'q': 2 * moments[0, :]**4 * moments[3, :],
'E': E_f}
axs_fluid, line_fluid = display_axes(case, dict_fluid, simul='fluid')
if 'Save' in case.Fluid:
data_f = case.output(0, [E_f, state_f], modes=case.output_modes)
if 'Plot' in case.Kinetic:
dict_kinetic = {'\\rho': moments[0, :],
'P': moments[0, :]**3 * moments[2, :],
'q': 2 * moments[0, :]**4 * moments[3, :],
'E': E_k}
axs_kinetic, line_kinetic = display_axes(case, dict_kinetic, simul='kinetic')
fig = plt.figure(figsize=(7, 6.5))
fig.canvas.manager.set_window_title(r'Distribution function f(x,v,t)')
ax_fxvt = plt.gca()
ax_fxvt.set_title('$\omega_p t = 0 $', loc='right', pad=-10)
im = plt.imshow(state_k.transpose(), interpolation='gaussian', origin='lower', aspect='auto', extent=(-case.Lx, case.Lx, -case.Lv, case.Lv), vmin=xp.min(state_k), vmax=xp.max(state_k))
plt.gca().set_xlabel('$x$')
plt.gca().set_ylabel('$v$')
plt.colorbar()
if 'Save' in case.Kinetic:
data_k = case.output(0, [E_k, moments[0:4,:].reshape(4*case.Nx)], modes=case.output_modes)
TimeStep = 1 / case.nsteps
t_eval = xp.linspace(1/case.nsteps, 1, case.nsteps)
start = time.time()
stop_fluid = False
for _ in trange(xp.int32(case.Tf)):
if 'Compute' in case.Fluid and not stop_fluid:
sol = solve_ivp(case.eqn_4f, (0, 1), state_f, t_eval=t_eval, method=case.integrator_fluid, atol=case.precision, rtol=case.precision)
if sol.status!=0:
print('\033[33m Warning: fluid simulation stopped before the end \033[00m')
stop_fluid = True
else:
state_f = sol.y[:, -1]
if xp.min(state_f[2*case.Nx:3*case.Nx]) <= case.precision:
print('\033[31m Error: fluid simulation with S2<0 \033[00m')
stop_fluid = True
if 'Save' in case.Fluid:
for t in range(case.nsteps):
E_f = case.E(sol.y[:case.Nx, t])
data_f = xp.vstack((data_f, case.output(_ + t_eval[t], [E_f, sol.y[:, t]], modes=case.output_modes)))
if 'Plot' in case.Fluid:
rho, u, G2, G3 = xp.split(state_f, 4)
E_f = case.E(rho)
line_fluid[0].set_ydata(rho)
line_fluid[3].set_ydata(E_f)
S = case.compute_S(G2, G3)[:2]
line_fluid[1].set_ydata(rho**3 * S[0])
line_fluid[2].set_ydata(2 * rho**4 * S[1])
update_axes(case, axs_fluid, _ + 1)
if 'Compute' in case.Kinetic:
for t in range(case.nsteps):
for coeff, type in zip(case.integr_coeff, case.integr_type):
if type == 1:
state_k, E_k = case.L1(state_k, E_k, coeff * TimeStep)
elif type == 2:
state_k, E_k = case.L2(state_k, E_k, coeff * TimeStep)
if 'Save' in case.Kinetic:
moments = case.compute_moments(state_k, 4)
data_k = xp.vstack((data_k, case.output(_ + (t+1) * TimeStep, [E_k, moments[0:4,:].reshape(4*case.Nx)], modes=case.output_modes)))
state_k[state_k<=case.precision] = 0
f_ = xp.pad(state_k, ((0, 1),), mode='wrap')
f_ *= case.f0 / simpson(simpson(f_, case.v_, axis=1), case.x_)
state_k = f_[:-1, :-1]
if 'Plot' in case.Kinetic:
moments = case.compute_moments(state_k, 3)
line_kinetic[0].set_ydata(moments[0, :])
line_kinetic[1].set_ydata(moments[0, :]**3 * moments[2, :])
line_kinetic[2].set_ydata(2 * moments[0, :]**4 * moments[3, :])
line_kinetic[3].set_ydata(E_k)
update_axes(case, axs_kinetic, _ + 1)
ax_fxvt.set_title('$\omega_p t = {{{}}}$'.format(_ + 1), loc='right', pad=-10)
im.set_data(state_k.transpose())
print('\033[90m Computation finished in {} seconds \033[00m'.format(int(time.time() - start)))
if 'Save' in case.Fluid:
save_data(state_f, data_f, timestr, case, model='Fluid')
if 'Save' in case.Kinetic:
save_data(state_k, data_k, timestr, case, model='Kinetic')
if 'Compute' in case.Kinetic:
H_k = case.energy_kinetic(state_k, E_k)
print('\033[90m Error in energy (kinetic) = {:.2e}'.format(xp.abs(H_k - H0_k)))
for indx, C in enumerate(case.casimirs_kinetic(state_k, case.n_casimirs)):
print('\033[90m Error in Casimir C{:d} (kinetic) = {:.2e}'.format(indx + 1, xp.abs(C - C0_k[indx])))
if 'Compute' in case.Fluid:
H = case.energy_fluid(state_f, E_f)
print('\033[90m Error in energy (fluid) = {:.2e}'.format(xp.abs(H - H0_f)))
for indx, C in enumerate(case.casimirs_fluid(state_f)):
print('\033[90m Error in Casimir C{:d} (fluid) = {:.2e}'.format(indx + 1, xp.abs(C - C0_f[indx])))
plt.ioff()
plt.show()
def display_axes(case, dict, simul='fluid'):
plt.ion()
if case.darkmode:
cs = ['k', 'w', 'c', 'm', 'r']
else:
cs = ['w', 'k', 'c', 'm', 'r']
plt.rc('figure', facecolor=cs[0], titlesize=30)
plt.rc('text', usetex=True, color=cs[1])
plt.rc('font', family='sans-serif', size=20)
plt.rc('axes', facecolor=cs[0], edgecolor=cs[1], labelsize=26, labelcolor=cs[1], titlecolor=cs[1])
plt.rc('xtick', color=cs[1], labelcolor=cs[1])
plt.rc('ytick', color=cs[1], labelcolor=cs[1])
plt.rc('lines', linewidth=3)
plt.rc('image', cmap='bwr')
fig = plt.figure(figsize=(8, 10))
fig.canvas.manager.set_window_title((simul + ' simulation').capitalize())
axs = fig.add_gridspec(len(dict), hspace=0.2).subplots(sharex=True)
line = []
for m, (key, value) in enumerate(dict.items()):
axs[m].plot(case.x, value, cs[m+1], linestyle='--', linewidth=1, label=r'$' + str(key) + '(x,0)$')
line_temp, = axs[m].plot(case.x, value, cs[m+1], label=r'$' + str(key) + '(x,t)$')
line.append(line_temp)
axs[0].set_title('$\omega_p t = 0 $', loc='right', pad=20)
for ax in axs:
ax.set_xlim((-case.Lx, case.Lx))
ax.legend(loc='upper right', labelcolor='linecolor')
axs[-1].set_xlabel('$x$')
plt.draw()
plt.pause(1e-4)
return axs, line
def update_axes(case, axs, t):
axs[0].set_title('$\omega_p t = {{{}}}$'.format(t), loc='right', pad=20)
for ax in axs:
ax.relim()
ax.autoscale()
ax.set_xlim((-case.Lx, case.Lx))
plt.draw()
plt.pause(1e-4)
def save_data(state, data, timestr, case, model=[]):
mdic = case.DictParams.copy()
mdic.update({'final': state, 'data': data})
date_today = date.today().strftime(" %B %d, %Y")
mdic.update({'date': date_today, 'author': 'cristel.chandre@cnrs.fr'})
name_file = type(case).__name__ + '_' + model + '_' + timestr + '.mat'
savemat(name_file, mdic)
print('\033[90m {} results saved in {} \033[00m'.format(model, name_file))