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Mischa Dombrowski
lbmweights
Commits
0698e79c
Commit
0698e79c
authored
Sep 08, 2019
by
MischaD
Browse files
Solution Expected Function
parent
674eea74
Changes
2
Hide whitespace changes
Inline
Sidebyside
lbmweights/lattice.py
View file @
0698e79c
...
...
@@ 9,13 +9,13 @@ from .shell import Shell
class
Lattice
:
BY_NAME
=
{
"D2Q9"
:
{
"dimension"
:
2
,
"order"
:
4
,
"shell_list"
:
[
1
,
2
,
4
]},
"D2V17"
:
{
"dimension"
:
2
,
"order"
:
6
,
"shell_list"
:
[
1
,
2
,
4
,
8
,
9
]},
"D2V37"
:
{
"dimension"
:
2
,
"order"
:
8
,
"shell_list"
:
[
1
,
2
,
4
,
5
,
8
,
9
,
10
,
16
]},
"D3Q19"
:
{
"dimension"
:
3
,
"order"
:
4
,
"shell_list"
:
[
1
,
2
,
4
]},
"D3Q15"
:
{
"dimension"
:
3
,
"order"
:
4
,
"shell_list"
:
[
1
,
3
,
4
]},
BY_NAME
=
{
"D2Q9"
:
{
"dimension"
:
2
,
"order"
:
4
,
"shell_list"
:
[
1
,
2
,
4
]
,
"seed"
:
44
},
"D2V17"
:
{
"dimension"
:
2
,
"order"
:
6
,
"shell_list"
:
[
1
,
2
,
4
,
8
,
9
]
,
"seed"
:
44
},
"D2V37"
:
{
"dimension"
:
2
,
"order"
:
8
,
"shell_list"
:
[
1
,
2
,
4
,
5
,
8
,
9
,
10
,
16
]
,
"seed"
:
44
},
"D3Q19"
:
{
"dimension"
:
3
,
"order"
:
4
,
"shell_list"
:
[
1
,
2
,
4
]
,
"seed"
:
44
},
"D3Q15"
:
{
"dimension"
:
3
,
"order"
:
4
,
"shell_list"
:
[
1
,
3
,
4
]
,
"seed"
:
44
},
"D3Q41ZOT"
:
{
"dimension"
:
3
,
"order"
:
6
,
"shell_list"
:
[
1
,
2
,
3
,
9
,
16
,
27
],
"boundary"
:
"sup"
,
"unwanted_subshells"
:
[
"221"
,
"511"
]},
"unwanted_subshells"
:
[
"221"
,
"511"
]
,
"seed"
:
44
},
}
def
__init__
(
self
,
dimension
=
2
,
order
=
4
,
shell_list
=
[
1
,
2
,
4
],
seed
=
None
,
boundary
=
None
,
unwanted_subshells
=
[],
svd_tolerance
=
1e8
):
...
...
@@ 83,16 +83,16 @@ class Lattice:
return
string
@
classmethod
def
from_name
(
cls
,
name
,
seed
=
None
):
def
from_name
(
cls
,
name
):
"""Initiate the Lattice with the correct values corresponding to a know Lattice in literature.
A complete list can be seen in Lattice.BY_NAME.keys()"""
kwargs
=
cls
.
BY_NAME
.
get
(
name
)
if
not
kwargs
:
raise
ValueError
(
"No Lattice with this name is known or implemented"
)
return
cls
(
**
kwargs
,
seed
=
seed
)
return
cls
(
**
kwargs
)
@
classmethod
def
from_order
(
cls
,
dimension
,
order
,
seed
=
None
):
def
from_order
(
cls
,
dimension
,
order
):
"""
:param dimension:
:param order:
...
...
@@ 227,13 +227,16 @@ class Lattice:
reduced_rhs
[
i
,
:]
=
rhs
[
i
,
:]
/
singular_value
if
cols

rows
>
0
:
# TODO Better
raise
InfiniteSolutionsException
(
"Reduce order, remove shells, or use continue.py in "
"https://github.com/BDuenweg/LatticeBoltzmannweights"
)
self
.
_solution
=
np
.
dot
(
np
.
transpose
(
V
),
reduced_rhs
)
return
self
.
_solution
def
_calculate_coefficients
(
self
):
"""Use _all_velocity_vectors and _solution to calculate the coefficients of the
weigth polynomials. Writes them into _coefficients
"""
solution_columns
=
self
.
_order
//
2
coefficients
=
np
.
zeros
((
1
+
solution_columns
))
coefficients
[
0
]
=
1
...
...
@@ 275,8 +278,13 @@ class Lattice:
self
.
_interval
=
sp
.
Complement
(
interval
,
sp
.
FiniteSet
(
0
))
return
self
.
_interval
def
calculate_polynomials
(
self
):
c_s_sq
=
sp
.
Symbol
(
"c_s_sq"
)
def
solution_expected
(
self
):
"""Evaluate if the order, dimension and amount of shells entered are expected to retrieve a solution.
This is in no way a guarantee on the existence of a solution or whether or not the program
will finish successful, but it can be used as a quick hint on the existence of a solution.
Changes the state of self._solution and self._velocity vectors for future calculations."""
if
self
.
_order
%
2
==
1
:
self
.
_order
=
1
logger
.
warning
(
"Only odd order valid. Decrease by one"
)
...
...
@@ 292,30 +300,32 @@ class Lattice:
self
.
_svd
()
self
.
_calculate_coefficients
()
return
self
.
_solution
is
not
None
apporx_coeffs
=
[[
approximate_ratio
(
x
)
for
x
in
pol_coffs
]
for
pol_coffs
in
self
.
_coefficients
]
def
calculate_polynomials
(
self
,
approximate
=
True
):
"""Main algorithm as proposed by D. Spiller and B Duenweg.
self
.
_weight_polynomials
=
[
sp
.
Poly
([
approximate_ratio
(
x
)
for
x
in
pol_coffs
],
c_s_sq
)
for
pol_coffs
in
self
.
_coefficients
]
if
not
self
.
_weight_polynomials
:
raise
NoSolutionException
(
"Something went wrong"
)
Divided into the part where the existence of a solution and calculated together with all the velocity
vectors. If one is expected the coefficients are calculated, the interval evaluated and the weight
polynomials returned.
self
.
_interval
=
self
.
_calculate_valid_interval
()
if
self
.
_interval
==
sp
.
EmptySet
():
return
[]
return
self
.
_weight_polynomials
:param approximate: Use python Fraction to approximate the calculated polynomial coefficients as rational
number. This should give better results, since they should have a rational representation.
def
calculate_reduced_weights
(
self
,
boundary
=
"inf"
):
"""
Calculate the weights of this lattice for a reduced model.
If the smallest or biggest value of the valid interval is taken, they reduce
the amount of shells necessary by one.
Overwrites the weight values in self.shell
:return: List of Sympy Polynomials."""
:param boundary: "inf" > smallest possible value is taken, otherwise the largest
:return: list of weights in the order of their shells.
"""
return
self
.
calculate_weights
(
boundary
=
boundary
)
self
.
solution_expected
()
self
.
_calculate_coefficients
()
c_s_sq
=
sp
.
Symbol
(
"c_s_sq"
)
if
approximate
:
self
.
_weight_polynomials
=
[
sp
.
Poly
([
approximate_ratio
(
x
)
for
x
in
pol_coffs
],
c_s_sq
)
for
pol_coffs
in
self
.
_coefficients
]
else
:
self
.
_weight_polynomials
=
[
sp
.
Poly
(
pol_coffs
,
c_s_sq
)
for
pol_coffs
in
self
.
_coefficients
]
self
.
_interval
=
self
.
_calculate_valid_interval
()
return
[]
if
self
.
_interval
==
sp
.
EmptySet
else
self
.
_weight_polynomials
def
calculate_weights
(
self
,
c_s_sq
=
None
,
boundary
=
None
):
"""
...
...
@@ 330,7 +340,7 @@ class Lattice:
:param c_s_sq: Float value for the speed of sound, has to be inside of the valid interval
:param boundary: Get reduced model by using the infimum or supremum of the interval. Fallback value if
no c_s_sq is given
:return:
:return:
weights With zero weight(s) included
"""
if
not
self
.
_weight_polynomials
:
...
...
@@ 358,9 +368,11 @@ class Lattice:
def
velocity_set
(
self
):
"""
Returns the values that are important for the Lattice Boltzmann Model, i.e.
Removes unwanted shells, i.e. weight == = and
returns the values that are important for the Lattice Boltzmann Model, i.e.
a list of the velocity values their corresponding weights and the value for the speed of sound.
:return: (c_s_sq, weights, velocities): c_s_sq
:return: (c_s_sq, weights, velocities)
"""
if
not
self
.
weights
:
self
.
calculate_weights
()
...
...
test/test_lattice.py
View file @
0698e79c
...
...
@@ 4,6 +4,16 @@ from lbmweights import Lattice
from
lbmweights.utils.mylog
import
logger
class
SolutionExpected
(
unittest
.
TestCase
):
def
setUp
(
self
):
pass
def
test_solution_expected
(
self
):
for
name
,
lattice_args
in
Lattice
.
BY_NAME
.
items
():
lattice
=
Lattice
(
**
lattice_args
)
self
.
assertTrue
(
lattice
.
solution_expected
())
class
TestQ9
(
unittest
.
TestCase
):
def
setUp
(
self
):
self
.
seed
=
20
...
...
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