def get_context():
"""Set up context for solver"""
# Get points and weights for Chebyshev weighted integrals
ST = ShenDirichletBasis(params.N[0], quad=params.Dquad)
SB = ShenBiharmonicBasis(params.N[0], quad=params.Bquad)
CT = ST.CT # Chebyshev transform
Nu = params.N[0]-2 # Number of velocity modes in Shen basis
Nb = params.N[0]-4 # Number of velocity modes in Shen biharmonic basis
u_slice = slice(0, Nu)
v_slice = slice(0, Nb)
FST = SlabShen_R2C(params.N, params.L, comm, threads=params.threads,
communication=params.communication,
planner_effort=params.planner_effort,
dealias_cheb=params.dealias_cheb)
float, complex, mpitype = datatypes("double")
ST.plan(FST.complex_shape(), 0, complex, {'threads':params.threads,
'planner_effort':params.planner_effort["dct"]})
SB.plan(FST.complex_shape(), 0, complex, {'threads':params.threads,
'planner_effort':params.planner_effort["dct"]})
# Mesh variables
X = FST.get_local_mesh(ST)
x0, x1, x2 = FST.get_mesh_dims(ST)
K = FST.get_local_wavenumbermesh(scaled=True)
K2 = K[1]*K[1]+K[2]*K[2]
K4 = K2**2
# Set Nyquist frequency to zero on K that is used for odd derivatives
Kx = FST.get_local_wavenumbermesh(scaled=True, eliminate_highest_freq=True)
K_over_K2 = zeros((2,) + FST.complex_shape())
for i in range(2):
K_over_K2[i] = K[i+1] / np.where(K2==0, 1, K2)
# Solution variables
U = zeros((3,)+FST.real_shape(), dtype=float)
U0 = zeros((3,)+FST.real_shape(), dtype=float)
U_hat = zeros((3,)+FST.complex_shape(), dtype=complex)
U_hat0 = zeros((3,)+FST.complex_shape(), dtype=complex)
g = zeros(FST.complex_shape(), dtype=complex)
# primary variable
u = (U_hat, g)
H_hat = zeros((3,)+FST.complex_shape(), dtype=complex)
H_hat0 = zeros((3,)+FST.complex_shape(), dtype=complex)
H_hat1 = zeros((3,)+FST.complex_shape(), dtype=complex)
dU = zeros((3,)+FST.complex_shape(), dtype=complex)
hv = zeros(FST.complex_shape(), dtype=complex)
hg = zeros(FST.complex_shape(), dtype=complex)
Source = zeros((3,)+FST.real_shape(), dtype=float)
Sk = zeros((3,)+FST.complex_shape(), dtype=complex)
work = work_arrays()
nu, dt, N = params.nu, params.dt, params.N
kx = K[0][:, 0, 0]
# Collect all linear algebra solvers
la = config.AttributeDict(dict(
HelmholtzSolverG = Helmholtz(N[0], np.sqrt(K2[0]+2.0/nu/dt), ST),
BiharmonicSolverU = Biharmonic(N[0], -nu*dt/2., 1.+nu*dt*K2[0],
-(K2[0] + nu*dt/2.*K4[0]), quad=SB.quad,
solver="cython"),
HelmholtzSolverU0 = Helmholtz(N[0], np.sqrt(2./nu/dt), ST),
TDMASolverD = TDMA(inner_product((ST, 0), (ST, 0)))
)
)
alfa = K2[0] - 2.0/nu/dt
# Collect all matrices
mat = config.AttributeDict(dict(
CDD = inner_product((ST, 0), (ST, 1)),
AB = HelmholtzCoeff(N[0], 1.0, -alfa, ST.quad),
AC = BiharmonicCoeff(N[0], nu*dt/2., (1. - nu*dt*K2[0]), -(K2[0] - nu*dt/2.*K4[0]), quad=SB.quad),
# Matrices for biharmonic equation
CBD = inner_product((SB, 0), (ST, 1)),
ABB = inner_product((SB, 0), (SB, 2)),
BBB = inner_product((SB, 0), (SB, 0)),
SBB = inner_product((SB, 0), (SB, 4)),
# Matrices for Helmholtz equation
ADD = inner_product((ST, 0), (ST, 2)),
BDD = inner_product((ST, 0), (ST, 0)),
BBD = inner_product((SB, 0), (ST, 0)),
CDB = inner_product((ST, 0), (SB, 1))
)
)
hdf5file = KMMWriter({"U":U[0], "V":U[1], "W":U[2]},
chkpoint={'current':{'U':U}, 'previous':{'U':U0}},
filename=params.solver+".h5",
mesh={"x": x0, "y": x1, "z": x2})
return config.AttributeDict(locals())
def get_context():
"""Set up context for solver"""
# Get points and weights for Chebyshev weighted integrals
assert params.Dquad == params.Bquad
collapse_fourier = False if params.dealias == '3/2-rule' else True
ST = Basis(params.N[0], 'C', bc=(0, 0), quad=params.Dquad)
SB = Basis(params.N[0], 'C', bc='Biharmonic', quad=params.Bquad)
CT = Basis(params.N[0], 'C', quad=params.Dquad)
ST0 = Basis(params.N[0], 'C', bc=(0, 0),
quad=params.Dquad) # For 1D problem
K0 = Basis(params.N[1], 'F', domain=(0, params.L[1]), dtype='D')
K1 = Basis(params.N[2], 'F', domain=(0, params.L[2]), dtype='d')
kw0 = {
'threads': params.threads,
'planner_effort': params.planner_effort["dct"],
'slab': (params.decomposition == 'slab'),
'collapse_fourier': collapse_fourier
}
FST = TensorProductSpace(comm, (ST, K0, K1), **kw0) # Dirichlet
FSB = TensorProductSpace(comm, (SB, K0, K1), **kw0) # Biharmonic
FCT = TensorProductSpace(comm, (CT, K0, K1), **kw0) # Regular Chebyshev
VFS = MixedTensorProductSpace([FSB, FST, FST])
VFST = MixedTensorProductSpace([FST, FST, FST])
VUG = MixedTensorProductSpace([FSB, FST])
# Padded
kw = {
'padding_factor': 1.5 if params.dealias == '3/2-rule' else 1,
'dealias_direct': params.dealias == '2/3-rule'
}
if params.dealias == '3/2-rule':
# Requires new bases due to planning and transforms on different size arrays
STp = Basis(params.N[0], 'C', bc=(0, 0), quad=params.Dquad)
SBp = Basis(params.N[0], 'C', bc='Biharmonic', quad=params.Bquad)
CTp = Basis(params.N[0], 'C', quad=params.Dquad)
else:
STp, SBp, CTp = ST, SB, CT
K0p = Basis(params.N[1], 'F', dtype='D', domain=(0, params.L[1]), **kw)
K1p = Basis(params.N[2], 'F', dtype='d', domain=(0, params.L[2]), **kw)
FSTp = TensorProductSpace(comm, (STp, K0p, K1p), **kw0)
FSBp = TensorProductSpace(comm, (SBp, K0p, K1p), **kw0)
FCTp = TensorProductSpace(comm, (CTp, K0p, K1p), **kw0)
VFSp = MixedTensorProductSpace([FSBp, FSTp, FSTp])
Nu = params.N[0] - 2 # Number of velocity modes in Shen basis
Nb = params.N[0] - 4 # Number of velocity modes in Shen biharmonic basis
u_slice = slice(0, Nu)
v_slice = slice(0, Nb)
float, complex, mpitype = datatypes("double")
# Mesh variables
X = FST.local_mesh(True)
x0, x1, x2 = FST.mesh()
K = FST.local_wavenumbers(scaled=True)
# Solution variables
U = Array(VFS)
U0 = Array(VFS)
U_hat = Function(VFS)
U_hat0 = Function(VFS)
g = Function(FST)
# primary variable
u = (U_hat, g)
H_hat = Function(VFST)
H_hat0 = Function(VFST)
H_hat1 = Function(VFST)
dU = Function(VUG)
hv = Function(FST)
hg = Function(FST)
Source = Array(VFS)
Sk = Function(VFS)
K2 = K[1] * K[1] + K[2] * K[2]
K4 = K2**2
# Set Nyquist frequency to zero on K that is used for odd derivatives in nonlinear terms
Kx = FST.local_wavenumbers(scaled=True, eliminate_highest_freq=True)
K_over_K2 = np.zeros((2, ) + g.shape)
for i in range(2):
K_over_K2[i] = K[i + 1] / np.where(K2 == 0, 1, K2)
for i in range(3):
K[i] = K[i].astype(float)
Kx[i] = K[i].astype(float)
work = work_arrays()
u_dealias = Array(VFSp)
u0_hat = np.zeros((2, params.N[0]), dtype=complex)
h0_hat = np.zeros((2, params.N[0]), dtype=complex)
w = np.zeros((params.N[0], ), dtype=complex)
w1 = np.zeros((params.N[0], ), dtype=complex)
nu, dt, N = params.nu, params.dt, params.N
alfa = K2[0] - 2.0 / nu / dt
# Collect all matrices
mat = config.AttributeDict(
dict(
CDD=inner_product((ST, 0), (ST, 1)),
AB=HelmholtzCoeff(N[0], 1., -(K2 - 2.0 / nu / dt), 0, ST.quad),
AC=BiharmonicCoeff(N[0], nu * dt / 2., (1. - nu * dt * K2),
-(K2 - nu * dt / 2. * K4), 0, SB.quad),
# Matrices for biharmonic equation
CBD=inner_product((SB, 0), (ST, 1)),
ABB=inner_product((SB, 0), (SB, 2)),
BBB=inner_product((SB, 0), (SB, 0)),
SBB=inner_product((SB, 0), (SB, 4)),
# Matrices for Helmholtz equation
ADD=inner_product((ST, 0), (ST, 2)),
BDD=inner_product((ST, 0), (ST, 0)),
BBD=inner_product((SB, 0), (ST, 0)),
CDB=inner_product((ST, 0), (SB, 1)),
ADD0=inner_product((ST0, 0), (ST0, 2)),
BDD0=inner_product((ST0, 0), (ST0, 0)),
))
la = config.AttributeDict(
dict(HelmholtzSolverG=Helmholtz(mat.ADD, mat.BDD, -np.ones((1, 1, 1)),
(K2 + 2.0 / nu / dt)),
BiharmonicSolverU=Biharmonic(mat.SBB, mat.ABB, mat.BBB,
-nu * dt / 2. * np.ones(
(1, 1, 1)), (1. + nu * dt * K2),
(-(K2 + nu * dt / 2. * K4))),
HelmholtzSolverU0=Helmholtz(mat.ADD0, mat.BDD0, np.array([-1.]),
np.array([2. / nu / dt])),
TDMASolverD=TDMA(inner_product((ST, 0), (ST, 0)))))
hdf5file = KMMFile(config.params.solver,
checkpoint={
'space': VFS,
'data': {
'0': {
'U': [U_hat]
},
'1': {
'U': [U_hat0]
}
}
},
results={
'space': VFS,
'data': {
'U': [U]
}
})
return config.AttributeDict(locals())
def get_context():
"""Set up context for solver"""
# Get points and weights for Chebyshev weighted integrals
ST = ShenDirichletBasis(params.N[0],
quad=params.Dquad,
threads=params.threads,
planner_effort=params.planner_effort["dct"])
SN = ShenNeumannBasis(params.N[0],
quad=params.Nquad,
threads=params.threads,
planner_effort=params.planner_effort["dct"])
CT = ST.CT
Nf = params.N[
2] / 2 + 1 # Number of independent complex wavenumbers in z-direction
Nu = params.N[0] - 2 # Number of velocity modes in Shen basis
Nq = params.N[0] - 3 # Number of pressure modes in Shen basis
u_slice = slice(0, Nu)
p_slice = slice(1, Nu)
FST = SlabShen_R2C(params.N,
params.L,
comm,
threads=params.threads,
communication=params.communication,
planner_effort=params.planner_effort,
dealias_cheb=params.dealias_cheb)
float, complex, mpitype = datatypes("double")
# Get grid for velocity points
X = FST.get_local_mesh(ST)
x0, x1, x2 = FST.get_mesh_dims(ST)
U = zeros((3, ) + FST.real_shape(), dtype=float)
U_hat = zeros((3, ) + FST.complex_shape(), dtype=complex)
P = zeros(FST.real_shape(), dtype=float)
P_hat = zeros(FST.complex_shape(), dtype=complex)
Pcorr = zeros(FST.complex_shape(), dtype=complex)
U0 = zeros((3, ) + FST.real_shape(), dtype=float)
U_hat0 = zeros((3, ) + FST.complex_shape(), dtype=complex)
U_hat1 = zeros((3, ) + FST.complex_shape(), dtype=complex)
dU = zeros((3, ) + FST.complex_shape(), dtype=complex)
H_hat = zeros((3, ) + FST.complex_shape(), dtype=complex)
H_hat0 = zeros((3, ) + FST.complex_shape(), dtype=complex)
H_hat1 = zeros((3, ) + FST.complex_shape(), dtype=complex)
diff0 = zeros((3, ) + FST.complex_shape(), dtype=complex)
Source = zeros((3, ) + FST.real_shape(), dtype=float)
Sk = zeros((3, ) + FST.complex_shape(), dtype=complex)
K = FST.get_local_wavenumbermesh(scaled=True)
K2 = K[1] * K[1] + K[2] * K[2]
K_over_K2 = zeros((3, ) + FST.complex_shape())
for i in range(3):
K_over_K2[i] = K[i] / np.where(K2 == 0, 1, K2)
work = work_arrays()
# Primary variable
u = (U_hat, P_hat)
nu, dt, N = params.nu, params.dt, params.N
# Collect all linear algebra solvers
la = config.AttributeDict(
dict(HelmholtzSolverU=Helmholtz(N[0], np.sqrt(K2[0] + 2.0 / nu / dt),
ST),
HelmholtzSolverP=Helmholtz(N[0], np.sqrt(K2[0]), SN),
TDMASolverD=TDMA(inner_product((ST, 0), (ST, 0))),
TDMASolverN=TDMA(inner_product((SN, 0), (SN, 0)))))
alfa = K2[0] - 2.0 / nu / dt
# Collect all matrices
kx = K[0][:, 0, 0]
mat = config.AttributeDict(
dict(CDN=inner_product((ST, 0), (SN, 1)),
CND=inner_product((SN, 0), (ST, 1)),
BDN=inner_product((ST, 0), (SN, 0)),
CDD=inner_product((ST, 0), (ST, 1)),
BDD=inner_product((ST, 0), (ST, 0)),
BDT=inner_product((ST, 0), (CT, 0)),
AB=HelmholtzCoeff(N[0], 1.0, -alfa, ST.quad)))
hdf5file = IPCSWriter({
"U": U[0],
"V": U[1],
"W": U[2],
"P": P
},
chkpoint={
'current': {
'U': U,
'P': P
},
'previous': {
'U': U0
}
},
filename=params.solver + ".h5",
mesh={
"x": x0,
"xp": FST.get_mesh_dim(SN, 0),
"y": x1,
"z": x2
})
return config.AttributeDict(locals())
def get_context():
"""Set up context for solver"""
# Get points and weights for Chebyshev weighted integrals
assert params.Dquad == params.Bquad
ST = ShenDirichletBasis(params.N[0], quad=params.Dquad)
SB = ShenBiharmonicBasis(params.N[0], quad=params.Bquad)
CT = Basis(params.N[0], quad=params.Dquad)
ST0 = ShenDirichletBasis(params.N[0], quad=params.Dquad, plan=True) # For 1D problem
K0 = C2CBasis(params.N[1], domain=(0, params.L[1]))
K1 = R2CBasis(params.N[2], domain=(0, params.L[2]))
FST = TensorProductSpace(comm, (ST, K0, K1), **{'threads':params.threads, 'planner_effort':params.planner_effort["dct"]}) # Dirichlet
FSB = TensorProductSpace(comm, (SB, K0, K1), **{'threads':params.threads, 'planner_effort':params.planner_effort["dct"]}) # Biharmonic
FCT = TensorProductSpace(comm, (CT, K0, K1), **{'threads':params.threads, 'planner_effort':params.planner_effort["dct"]}) # Regular Chebyshev
VFS = VectorTensorProductSpace([FSB, FST, FST])
# Padded
kw = {'padding_factor': 1.5 if params.dealias == '3/2-rule' else 1,
'dealias_direct': params.dealias == '2/3-rule'}
if params.dealias == '3/2-rule':
# Requires new bases due to planning and transforms on different size arrays
STp = ShenDirichletBasis(params.N[0], quad=params.Dquad)
SBp = ShenBiharmonicBasis(params.N[0], quad=params.Bquad)
CTp = Basis(params.N[0], quad=params.Dquad)
else:
STp, SBp, CTp = ST, SB, CT
K0p = C2CBasis(params.N[1], domain=(0, params.L[1]), **kw)
K1p = R2CBasis(params.N[2], domain=(0, params.L[2]), **kw)
FSTp = TensorProductSpace(comm, (STp, K0p, K1p), **{'threads':params.threads, 'planner_effort':params.planner_effort["dct"]})
FSBp = TensorProductSpace(comm, (SBp, K0p, K1p), **{'threads':params.threads, 'planner_effort':params.planner_effort["dct"]})
FCTp = TensorProductSpace(comm, (CTp, K0p, K1p), **{'threads':params.threads, 'planner_effort':params.planner_effort["dct"]})
VFSp = VectorTensorProductSpace([FSBp, FSTp, FSTp])
Nu = params.N[0]-2 # Number of velocity modes in Shen basis
Nb = params.N[0]-4 # Number of velocity modes in Shen biharmonic basis
u_slice = slice(0, Nu)
v_slice = slice(0, Nb)
float, complex, mpitype = datatypes("double")
# Mesh variables
X = FST.local_mesh(True)
x0, x1, x2 = FST.mesh()
K = FST.local_wavenumbers(scaled=True)
# Solution variables
U = Array(VFS, False)
U0 = Array(VFS, False)
U_hat = Array(VFS)
U_hat0 = Array(VFS)
g = Array(FST)
# primary variable
u = (U_hat, g)
H_hat = Array(VFS)
H_hat0 = Array(VFS)
H_hat1 = Array(VFS)
dU = Array(VFS)
hv = Array(FST)
hg = Array(FST)
Source = Array(VFS, False)
Sk = Array(VFS)
K2 = K[1]*K[1]+K[2]*K[2]
K4 = K2**2
# Set Nyquist frequency to zero on K that is used for odd derivatives in nonlinear terms
Kx = FST.local_wavenumbers(scaled=True, eliminate_highest_freq=True)
K_over_K2 = np.zeros((2,)+g.shape)
for i in range(2):
K_over_K2[i] = K[i+1] / np.where(K2 == 0, 1, K2)
work = work_arrays()
nu, dt, N = params.nu, params.dt, params.N
alfa = K2[0] - 2.0/nu/dt
# Collect all matrices
mat = config.AttributeDict(
dict(CDD=inner_product((ST, 0), (ST, 1)),
AB=HelmholtzCoeff(N[0], 1.0, -alfa, ST.quad),
AC=BiharmonicCoeff(N[0], nu*dt/2., (1. - nu*dt*K2[0]), -(K2[0] - nu*dt/2.*K4[0]), quad=SB.quad),
# Matrices for biharmonic equation
CBD=inner_product((SB, 0), (ST, 1)),
ABB=inner_product((SB, 0), (SB, 2)),
BBB=inner_product((SB, 0), (SB, 0)),
SBB=inner_product((SB, 0), (SB, 4)),
# Matrices for Helmholtz equation
ADD=inner_product((ST, 0), (ST, 2)),
BDD=inner_product((ST, 0), (ST, 0)),
BBD=inner_product((SB, 0), (ST, 0)),
CDB=inner_product((ST, 0), (SB, 1)),
ADD0=inner_product((ST0, 0), (ST0, 2)),
BDD0=inner_product((ST0, 0), (ST0, 0)),))
## Collect all linear algebra solvers
#la = config.AttributeDict(dict(
#HelmholtzSolverG = old_Helmholtz(N[0], np.sqrt(K2[0]+2.0/nu/dt), ST),
#BiharmonicSolverU = old_Biharmonic(N[0], -nu*dt/2., 1.+nu*dt*K2[0],
#-(K2[0] + nu*dt/2.*K4[0]), quad=SB.quad,
#solver="cython"),
#HelmholtzSolverU0 = old_Helmholtz(N[0], np.sqrt(2./nu/dt), ST),
#TDMASolverD = TDMA(inner_product((ST, 0), (ST, 0)))
#)
#)
mat.ADD.axis = 0
mat.BDD.axis = 0
mat.SBB.axis = 0
la = config.AttributeDict(
dict(HelmholtzSolverG=Helmholtz(mat.ADD, mat.BDD, -np.ones((1, 1, 1)),
(K2[0]+2.0/nu/dt)[np.newaxis, :, :]),
BiharmonicSolverU=Biharmonic(mat.SBB, mat.ABB, mat.BBB, -nu*dt/2.*np.ones((1, 1, 1)),
(1.+nu*dt*K2[0])[np.newaxis, :, :],
(-(K2[0] + nu*dt/2.*K4[0]))[np.newaxis, :, :]),
HelmholtzSolverU0=old_Helmholtz(N[0], np.sqrt(2./nu/dt), ST),
TDMASolverD=TDMA(inner_product((ST, 0), (ST, 0)))))
hdf5file = KMMWriter({"U":U[0], "V":U[1], "W":U[2]},
chkpoint={'current':{'U':U}, 'previous':{'U':U0}},
filename=params.solver+".h5",
mesh={"x": x0, "y": x1, "z": x2})
return config.AttributeDict(locals())