def scheme_constructor(ux, uy, s, s3):
la = 1.
dico = {
'dim':
2,
'scheme_velocity':
la,
'parameters': {
LA: la
},
'schemes': [
{
'velocities': list(range(1, 5)),
'conserved_moments': u,
'polynomials': [1, LA * X, LA * Y, LA**2 * (X**2 - Y**2)],
'relaxation_parameters': [0., s, s, s3],
'equilibrium': [u, ux * u, uy * u, 0.],
},
],
'stability': {
'test_maximum_principle': False,
'test_L2_stability': False,
},
}
return pyLBM.Scheme(dico)
def scheme_constructor(ux, uy, s_mu, s_eta):
rhoo = 1.
la = 1.
s3 = s_mu
s4 = s3
s5 = s4
s6 = s4
s7 = s_eta
s8 = s7
s = [0., 0., 0., s3, s4, s5, s6, s7, s8]
dummy = 1. / (LA**2 * rhoo)
qx2 = dummy * qx**2
qy2 = dummy * qy**2
q2 = qx2 + qy2
qxy = dummy * qx * qy
dico = {
'dim':
2,
'scheme_velocity':
la,
'parameters': {
LA: la
},
'schemes': [
{
'velocities':
list(range(9)),
'conserved_moments': [rho, qx, qy],
'polynomials': [
1, LA * X, LA * Y, 3 * (X**2 + Y**2) - 4,
0.5 * (9 * (X**2 + Y**2)**2 - 21 * (X**2 + Y**2) + 8),
3 * X * (X**2 + Y**2) - 5 * X,
3 * Y * (X**2 + Y**2) - 5 * Y, X**2 - Y**2, X * Y
],
'relaxation_parameters':
s,
'equilibrium': [
rho, qx, qy, -2 * rho + 3 * q2, rho + 1.5 * q2, -qx / LA,
-qy / LA, qx2 - qy2, qxy
],
},
],
'stability': {
'linearization': {
rho: rhoo,
qx: ux,
qy: uy
},
'test_maximum_principle': False,
'test_L2_stability': False,
},
}
return pyLBM.Scheme(dico)
def scheme_constructor(ux, sq, sE):
dico = {
'dim':
1,
'scheme_velocity':
1.,
'schemes': [
{
'velocities': list(range(3)),
'conserved_moments': u,
'polynomials': [1, X, X**2],
'equilibrium': [u, ux * u, (2 * ux**2 + 1) / 3 * u],
'relaxation_parameters': [0., sq, sE],
},
],
'stability': {
'test_maximum_principle': False,
'test_L2_stability': False,
},
}
return pyLBM.Scheme(dico)
# Loic Gouarin <*****@*****.**>
# Benjamin Graille <*****@*****.**>
#
# License: BSD 3 clause
"""
Example of a 6 velocities scheme for the advection equation in 3D
"""
from six.moves import range
import sympy as sp
import pyLBM
u, X, Y, Z = sp.symbols('u,X,Y,Z')
cx, cy, cz = .1, .0, .0
d = {
'dim':
3,
'scheme_velocity':
1.,
'schemes': [
{
'velocities': list(range(1, 7)),
'conserved_moments': u,
'polynomials': [1, X, Y, Z, X**2 - Y**2, X**2 - Z**2],
'equilibrium': [u, cx * u, cy * u, cz * u, 0., 0.],
'relaxation_parameters': [0., 1.9, 1.9, 1.9, 1.2, 1.2],
},
],
}
s = pyLBM.Scheme(d)
print(s)
print(s.generator.code)
def construct_scheme(module, dico):
s = pyLBM.Scheme(dico)
for m1, m2 in zip(s.Mnum, module.Mnum):
tools.ok_(np.all(m1 == m2))
tools.eq_(s._EQ, module.EQ_result)
{
'velocities':
range(9),
'conserved_moments': [rho, qx, qy],
'polynomials': [
1, LA * X, LA * Y, 3 * (X**2 + Y**2) - 4,
(9 * (X**2 + Y**2)**2 - 21 * (X**2 + Y**2) + 8) / 2,
3 * X * (X**2 + Y**2) - 5 * X, 3 * Y * (X**2 + Y**2) - 5 * Y,
X**2 - Y**2, X * Y
],
'relaxation_parameters':
s,
'equilibrium': [
rho, qx, qy, -2 * rho + 3 * q2, rho - 3 * q2, -qx / LA,
-qy / LA, qx2 - qy2, qxy
],
},
],
'consistency': {
'order': 2,
'linearization': {
rho: 1,
qx: 0,
qy: 0
},
#'linearization':{rho: rhoo, qx: rhoo*ux, qy: rhoo*uy},
},
}
S = pyLBM.Scheme(dico)