Commit f58d60c4 authored by RudolfWeeber's avatar RudolfWeeber
Browse files

Test for fluctuating LB, avg temperature and velocity distribution

parent d4679714
Pipeline #19917 failed with stage
in 5 minutes and 12 seconds
"""
This tests that for the thermalized LB (MRT with 15 equal relaxation times),
the correct temperature is obtained and the velocity distribution matches
the Maxwell-Boltzmann distribution
"""
import pystencils as ps
from lbmpy.lbstep import LatticeBoltzmannStep
from lbmpy.creationfunctions import create_lb_collision_rule
from lbmpy.relaxationrates import relaxation_rate_from_lattice_viscosity, relaxation_rate_from_magic_number
import numpy as np
import pickle
import gzip
from time import time
def single_component_maxwell(x1, x2, kT):
"""Integrate the probability density from x1 to x2 using the trapezoidal rule"""
x = np.linspace(x1, x2, 1000)
return np.trapz(np.exp(-x**2 / (2. * kT)), x) / np.sqrt(2. * np.pi * kT)
def run_scenario(scenario, steps):
scenario.pre_run()
for t in range(scenario.time_steps_run, scenario.time_steps_run + steps):
scenario.kernel_params['time_step'] = t
scenario.time_step()
scenario.post_run()
scenario.time_steps_run += steps
def create_scenario(domain_size, temperature=None, viscosity=None, seed=2, target='cpu', openmp=4, method=None, num_rel_rates=None):
rr = [relaxation_rate_from_lattice_viscosity(viscosity)]
rr = rr*num_rel_rates
cr = create_lb_collision_rule(
stencil='D3Q19', compressible=True,
method=method, relaxation_rates=rr,
fluctuating={'temperature': temperature, 'seed': seed},
optimization={'cse_global': True, 'split': False,
'cse_pdfs': True, 'vectorization': True}
)
return LatticeBoltzmannStep(periodicity=(True, True, True), domain_size=domain_size, compressible=True, stencil='D3Q19', collision_rule=cr, optimization={'target': target, 'openmp': openmp})
def run_for_method(method, num_rel_rates):
print("Testing", method)
# Unit conversions (MD to lattice) for parameters known to work with Espresso
agrid = 1.
m = 1. # mass per node
tau = 0.01 # time step
temperature = 4. / (m * agrid**2/tau**2)
viscosity = 3. * tau / agrid**2
n = 8
sc = create_scenario((n, n, n), viscosity=viscosity, temperature=temperature,
target='cpu', openmp=4, method=method, num_rel_rates=num_rel_rates)
assert np.average(sc.velocity[:, :, :]) == 0.
# Warmup
run_scenario(sc, steps=500)
# sampling:
steps = 20000
v = np.zeros((steps, n, n, n, 3))
for i in range(steps):
run_scenario(sc, steps=2)
v[i, :, :, :, :] = np.copy(sc.velocity[:, :, :, :])
v = v.reshape((steps*n*n*n, 3))
np.testing.assert_allclose(np.mean(v, axis=0), [0, 0, 0], atol=6E-7)
np.testing.assert_allclose(
np.var(v, axis=0), [temperature, temperature, temperature], rtol=1E-2)
v_hist, v_bins = np.histogram(v, bins=11, range=(-.08, .08), density=True)
# Calculate expected values from single
v_expected = []
for i in range(len(v_hist)):
# Maxwell distribution
res = np.exp(-v_bins[i]**2/(2.*temperature)) / \
np.sqrt(2*np.pi*temperature)
res = 1./(v_bins[i+1]-v_bins[i]) * \
single_component_maxwell(v_bins[i], v_bins[i+1], temperature)
v_expected.append(res)
v_expected = np.array(v_expected)
# 8% accuracy on the entire histogram
np.testing.assert_allclose(v_hist, v_expected, rtol=0.08)
# 0.5% accuracy on the middle part
remove = 3
np.testing.assert_allclose(
v_hist[remove:-remove], v_expected[remove:-remove], rtol=0.005)
def test_mrt():
run_for_method('mrt', 15)
Markdown is supported
0% or .
You are about to add 0 people to the discussion. Proceed with caution.
Finish editing this message first!
Please register or to comment