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# Copyright (C) 2008 Andreas Kloeckner
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program. If not, see <http://www.gnu.org/licenses/>.
from __future__ import division
import numpy
import numpy.linalg as la
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class UniformMachFlow:
def __init__(self, mach=0.1, p=1, rho=1, reynolds=100,
gamma=1.4, prandtl=0.72, char_length=1, spec_gas_const=287.1,
angle_of_attack=None, direction=None, gaussian_pulse_at=None,
pulse_magnitude=0.1):
"""
:param direction: is a vector indicating the direction of the
flow. Only one of angle_of_attack and direction may be
specified. Only the direction, not the magnitude, of
direction is taken into account.
:param angle_of_attack: if not None, specifies the angle of
the flow along the Y axis, where the flow is
directed along the X axis.
"""
if angle_of_attack is not None and direction is not None:
raise ValueError("Only one of angle_of_attack and "
"direction may be specified.")
if angle_of_attack is None and direction is None:
angle_of_attack = 0
if direction is not None:
self.direction = direction/la.norm(direction)
else:
self.direction = None
self.mach = mach
self.p = p
self.rho = rho
self.gamma = gamma
self.prandtl = prandtl
self.reynolds = reynolds
self.length = char_length
self.spec_gas_const = spec_gas_const
self.angle_of_attack = angle_of_attack
self.gaussian_pulse_at = gaussian_pulse_at
self.pulse_magnitude = pulse_magnitude
self.c = (self.gamma * p / rho)**0.5
u = self.velocity = mach * self.c
self.e = p / (self.gamma - 1) + rho / 2 * u**2
if numpy.isinf(self.reynolds):
self.mu = 0
else:
self.mu = u * self.length * rho / self.reynolds
def direction_vector(self, dimensions):
# this must be done here because dimensions is not known above
if self.direction is None:
assert self.angle_of_attack is not None
direction = numpy.zeros(dimensions, dtype=numpy.float64)
direction[0] = numpy.cos(
self.angle_of_attack / 180. * numpy.pi)
direction[1] = numpy.sin(
self.angle_of_attack / 180. * numpy.pi)
return direction
else:
return self.direction
def __call__(self, t, x_vec):
ones = numpy.ones_like(x_vec[0])
rho_field = ones*self.rho
if self.gaussian_pulse_at is not None:
rel_to_pulse = [x_vec[i] - self.gaussian_pulse_at[i]
for i in range(len(x_vec))]
rho_field += self.pulse_magnitude * self.rho * numpy.exp(
- sum(rtp_i**2 for rtp_i in rel_to_pulse)/2)
direction = self.direction_vector(x_vec.shape[0])
u_field = make_obj_array([ones*self.velocity*dir_i
for dir_i in direction])
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return join_fields(rho_field, self.e*ones, self.rho*u_field)
def volume_interpolant(self, t, discr):
return discr.convert_volume(
self(t, discr.nodes.T),
kind=discr.compute_kind,
dtype=discr.default_scalar_type)
def boundary_interpolant(self, t, discr, tag):
return discr.convert_boundary(
self(t, discr.get_boundary(tag).nodes.T),
tag=tag, kind=discr.compute_kind,
dtype=discr.default_scalar_type)
class Vortex:
def __init__(self):
self.beta = 5
self.gamma = 1.4
self.center = numpy.array([5, 0])
self.velocity = numpy.array([1, 0])
self.mu = 0
self.prandtl = 0.72
self.spec_gas_const = 287.1
def __call__(self, t, x_vec):
vortex_loc = self.center + t*self.velocity
# coordinates relative to vortex center
x_rel = x_vec[0] - vortex_loc[0]
y_rel = x_vec[1] - vortex_loc[1]
# Y.C. Zhou, G.W. Wei / Journal of Computational Physics 189 (2003) 159
# also JSH/TW Nodal DG Methods, p. 209
from math import pi
r = numpy.sqrt(x_rel**2+y_rel**2)
expterm = self.beta*numpy.exp(1-r**2)
u = self.velocity[0] - expterm*y_rel/(2*pi)
v = self.velocity[1] + expterm*x_rel/(2*pi)
rho = (1-(self.gamma-1)/(16*self.gamma*pi**2)*expterm**2)**(1/(self.gamma-1))
p = rho**self.gamma
e = p/(self.gamma-1) + rho/2*(u**2+v**2)
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return join_fields(rho, e, rho*u, rho*v)
def volume_interpolant(self, t, discr):
return discr.convert_volume(
self(t, discr.nodes.T
.astype(discr.default_scalar_type)),
kind=discr.compute_kind)
def boundary_interpolant(self, t, discr, tag):
return discr.convert_boundary(
self(t, discr.get_boundary(tag).nodes.T
.astype(discr.default_scalar_type)),
tag=tag, kind=discr.compute_kind)
class Vortex:
def __init__(self):
self.beta = 5
self.gamma = 1.4
self.center = numpy.array([5, 0])
self.velocity = numpy.array([1, 0])
self.final_time = 0.5
self.mu = 0
self.prandtl = 0.72
self.spec_gas_const = 287.1
def __call__(self, t, x_vec):
vortex_loc = self.center + t*self.velocity
# coordinates relative to vortex center
x_rel = x_vec[0] - vortex_loc[0]
y_rel = x_vec[1] - vortex_loc[1]
# Y.C. Zhou, G.W. Wei / Journal of Computational Physics 189 (2003) 159
# also JSH/TW Nodal DG Methods, p. 209
from math import pi
r = numpy.sqrt(x_rel**2+y_rel**2)
expterm = self.beta*numpy.exp(1-r**2)
u = self.velocity[0] - expterm*y_rel/(2*pi)
v = self.velocity[1] + expterm*x_rel/(2*pi)
rho = (1-(self.gamma-1)/(16*self.gamma*pi**2)*expterm**2)**(1/(self.gamma-1))
p = rho**self.gamma
e = p/(self.gamma-1) + rho/2*(u**2+v**2)
return join_fields(rho, e, rho*u, rho*v)
def volume_interpolant(self, t, discr):
return discr.convert_volume(
self(t, discr.nodes.T
.astype(discr.default_scalar_type)),
kind=discr.compute_kind)
def boundary_interpolant(self, t, discr, tag):
return discr.convert_boundary(
self(t, discr.get_boundary(tag).nodes.T
.astype(discr.default_scalar_type)),
tag=tag, kind=discr.compute_kind)