def apply_pressure(self, density_vec_sym, dir_vec_sym, mu_sym, qbx_forced_limit):
""" Symbolic expression for pressure field associated with the stresslet"""
import itertools
from pytential.symbolic.mappers import DerivativeTaker
kernel = LaplaceKernel(dim=self.dim)
factor = (2. * mu_sym)
for i, j in itertools.product(range(self.dim), range(self.dim)):
if i + j < 1:
sym_expr = factor * DerivativeTaker(i).map_int_g(
DerivativeTaker(j).map_int_g(
sym.S(kernel, density_vec_sym[i] * dir_vec_sym[j],
qbx_forced_limit=qbx_forced_limit)))
else:
sym_expr = sym_expr + (
factor * DerivativeTaker(i).map_int_g(
DerivativeTaker(j).map_int_g(
sym.S(kernel,
density_vec_sym[i] * dir_vec_sym[j],
qbx_forced_limit=qbx_forced_limit))))
return sym_expr
def apply_derivative(self, deriv_dir, density_vec_sym, dir_vec_sym, mu_sym,
qbx_forced_limit):
""" Symbolic derivative of velocity from stresslet.
Returns an object array of symbolic expressions for the vector
resulting from integrating the *deriv_dir* derivative of the
dyadic stresslet kernel (wrt target, not source) with
variable *density_vec_sym* and source direction vectors *dir_vec_sym*.
:arg deriv_dir: which derivative we want: 0, 1, or 2 for x, y, z
:arg density_vec_sym: a symbolic vector variable for the density vector
:arg dir_vec_sym: a symbolic vector variable for the normal direction
:arg mu_sym: a symbolic variable for the viscosity
:arg qbx_forced_limit: the qbx_forced_limit argument to be passed
on to IntG. +/-1 for exterior/interior one-sided boundary limit,
+/-2 for exterior/interior off-boundary evaluation, and 'avg'
for the average of the two one-sided boundary limits.
"""
import itertools
from pytential.symbolic.mappers import DerivativeTaker
sym_expr = np.empty((self.dim, ), dtype=object)
for comp in range(self.dim):
# Start variable count for kernel with 1 for the requested result
# component
base_count = np.zeros(self.dim, dtype=np.int)
base_count[comp] += 1
for i, j in itertools.product(range(self.dim), range(self.dim)):
var_ctr = base_count.copy()
var_ctr[i] += 1
var_ctr[j] += 1
ctr_key = tuple(var_ctr)
if i + j < 1:
sym_expr[comp] = DerivativeTaker(deriv_dir).map_int_g(
sym.IntG(self.kernel_dict[ctr_key],
dir_vec_sym[i] * density_vec_sym[j],
qbx_forced_limit=qbx_forced_limit,
mu=mu_sym))
else:
sym_expr[comp] = sym_expr[comp] + DerivativeTaker(
deriv_dir).map_int_g(
sym.IntG(self.kernel_dict[ctr_key],
dir_vec_sym[i] * density_vec_sym[j],
qbx_forced_limit=qbx_forced_limit,
mu=mu_sym))
return sym_expr
def apply_derivative(self, deriv_dir, density_vec_sym, dir_vec_sym, mu_sym,
qbx_forced_limit):
"""Symbolic derivative of velocity from stresslet.
Returns an object array of symbolic expressions for the vector
resulting from integrating the *deriv_dir* target derivative of the
dyadic Stresslet kernel with variable *density_vec_sym* and source
direction vectors *dir_vec_sym*.
:arg deriv_dir: integer denoting the axis direction for the derivative.
:arg density_vec_sym: a symbolic vector variable for the density vector.
:arg dir_vec_sym: a symbolic vector variable for the normal direction.
:arg mu_sym: a symbolic variable for the viscosity.
:arg qbx_forced_limit: the *qbx_forced_limit* argument to be passed on
to :class:`~pytential.symbolic.primitives.IntG`.
"""
import itertools
from pytential.symbolic.mappers import DerivativeTaker
sym_expr = np.empty((self.dim, ), dtype=object)
for comp in range(self.dim):
# Start variable count for kernel with 1 for the requested result
# component
base_count = np.zeros(self.dim, dtype=np.int32)
base_count[comp] += 1
for i, j in itertools.product(range(self.dim), range(self.dim)):
var_ctr = base_count.copy()
var_ctr[i] += 1
var_ctr[j] += 1
ctr_key = tuple(var_ctr)
if i + j < 1:
sym_expr[comp] = DerivativeTaker(deriv_dir).map_int_g(
sym.int_g_vec(self.kernel_dict[ctr_key],
dir_vec_sym[i] * density_vec_sym[j],
qbx_forced_limit=qbx_forced_limit,
mu=mu_sym))
else:
sym_expr[comp] = sym_expr[comp] + DerivativeTaker(
deriv_dir).map_int_g(
sym.int_g_vec(self.kernel_dict[ctr_key],
dir_vec_sym[i] * density_vec_sym[j],
qbx_forced_limit=qbx_forced_limit,
mu=mu_sym))
return sym_expr
def apply_pressure(self, density_vec_sym, mu_sym, qbx_forced_limit):
""" Symbolic expression for pressure field associated with the Stokeslet"""
from pytential.symbolic.mappers import DerivativeTaker
kernel = LaplaceKernel(dim=self.dim)
for i in range(self.dim):
if i < 1:
sym_expr = DerivativeTaker(i).map_int_g(
sym.S(kernel, density_vec_sym[i],
qbx_forced_limit=qbx_forced_limit))
else:
sym_expr = sym_expr + (DerivativeTaker(i).map_int_g(
sym.S(kernel, density_vec_sym[i],
qbx_forced_limit=qbx_forced_limit)))
return sym_expr