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RudolfWeeber
lbmpy
Commits
f58d60c4
Commit
f58d60c4
authored
Nov 20, 2019
by
RudolfWeeber
Browse files
Test for fluctuating LB, avg temperature and velocity distribution
parent
d4679714
Pipeline
#19917
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in 5 minutes and 12 seconds
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lbmpy_tests/test_fluctuating_lb.py
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"""
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
)
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