__copyright__ = "Copyright (C) 2008 Andreas Kloeckner"
__license__ = """
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in
all copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
THE SOFTWARE.
"""
from __future__ import division
from __future__ import absolute_import
from __future__ import print_function
import numpy
import numpy.linalg as la
# modifies isentropic vortex solution so that rho->Arho, P->A^gamma rho^gamma
# this will be analytic solution if appropriate source terms are added
# to the RHS. coded for vel_x=1, vel_y=0
class Vortex:
def __init__(self, beta, gamma, center, velocity, densityA):
self.beta = beta
self.gamma = gamma
self.center = numpy.asarray(center)
self.velocity = numpy.asarray(velocity)
self.densityA = densityA
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 = self.densityA*(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)
from grudge.tools import join_fields
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 SourceTerms:
def __init__(self, beta, gamma, center, velocity, densityA):
self.beta = beta
self.gamma = gamma
self.center = numpy.asarray(center)
self.velocity = numpy.asarray(velocity)
self.densityA = densityA
def __call__(self,t,x_vec,q):
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]
# sources written in terms of A=1.0 solution
# (standard isentropic vortex)
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
#computed necessary derivatives
expterm_t = 2*expterm*x_rel
expterm_x = -2*expterm*x_rel
expterm_y = -2*expterm*y_rel
u_x = -expterm*y_rel/(2*pi)*(-2*x_rel)
v_y = expterm*x_rel/(2*pi)*(-2*y_rel)
#derivatives for rho (A=1)
facG=self.gamma-1
rho_t = (1/facG)*(1-(facG)/(16*self.gamma*pi**2)*expterm**2)**(1/facG-1)* \
(-facG/(16*self.gamma*pi**2)*2*expterm*expterm_t)
rho_x = (1/facG)*(1-(facG)/(16*self.gamma*pi**2)*expterm**2)**(1/facG-1)* \
(-facG/(16*self.gamma*pi**2)*2*expterm*expterm_x)
rho_y = (1/facG)*(1-(facG)/(16*self.gamma*pi**2)*expterm**2)**(1/facG-1)* \
(-facG/(16*self.gamma*pi**2)*2*expterm*expterm_y)
#derivatives for rho (A=1) to the power of gamma
rho_gamma_t = self.gamma*rho**(self.gamma-1)*rho_t
rho_gamma_x = self.gamma*rho**(self.gamma-1)*rho_x
rho_gamma_y = self.gamma*rho**(self.gamma-1)*rho_y
factorA=self.densityA**self.gamma-self.densityA
#construct source terms
source_rho = x_vec[0]-x_vec[0]
source_e = (factorA/(self.gamma-1))*(rho_gamma_t + self.gamma*(u_x*rho**self.gamma+u*rho_gamma_x)+ \
self.gamma*(v_y*rho**self.gamma+v*rho_gamma_y))
source_rhou = factorA*rho_gamma_x
source_rhov = factorA*rho_gamma_y
from grudge.tools import join_fields
return join_fields(source_rho, source_e, source_rhou, source_rhov, x_vec[0]-x_vec[0])
def volume_interpolant(self,t,q,discr):
return discr.convert_volume(
self(t,discr.nodes.T,q),
kind=discr.compute_kind)
def main(write_output=True):
from grudge.backends import guess_run_context
rcon = guess_run_context(
#["cuda"]
)
gamma = 1.4
# at A=1 we have case of isentropic vortex, source terms
# arise for other values
densityA = 2.0
from grudge.tools import EOCRecorder, to_obj_array
eoc_rec = EOCRecorder()
if rcon.is_head_rank:
from grudge.mesh import \
make_rect_mesh, \
make_centered_regular_rect_mesh
refine = 1
mesh = make_centered_regular_rect_mesh((0,-5), (10,5), n=(9,9),
post_refine_factor=refine)
mesh_data = rcon.distribute_mesh(mesh)
else:
mesh_data = rcon.receive_mesh()
for order in [4,5]:
discr = rcon.make_discretization(mesh_data, order=order,
debug=[#"cuda_no_plan",
#"print_op_code"
],
default_scalar_type=numpy.float64)
from grudge.visualization import SiloVisualizer, VtkVisualizer
#vis = VtkVisualizer(discr, rcon, "vortex-%d" % order)
vis = SiloVisualizer(discr, rcon)
vortex = Vortex(beta=5, gamma=gamma,
center=[5,0],
velocity=[1,0], densityA=densityA)
fields = vortex.volume_interpolant(0, discr)
sources=SourceTerms(beta=5, gamma=gamma,
center=[5,0],
velocity=[1,0], densityA=densityA)
from grudge.models.gas_dynamics import (
GasDynamicsOperator, GammaLawEOS)
from grudge.mesh import BTAG_ALL
op = GasDynamicsOperator(dimensions=2,
mu=0.0, prandtl=0.72, spec_gas_const=287.1,
equation_of_state=GammaLawEOS(vortex.gamma),
bc_inflow=vortex, bc_outflow=vortex, bc_noslip=vortex,
inflow_tag=BTAG_ALL, source=sources)
euler_ex = op.bind(discr)
max_eigval = [0]
def rhs(t, q):
ode_rhs, speed = euler_ex(t, q)
max_eigval[0] = speed
return ode_rhs
rhs(0, fields)
if rcon.is_head_rank:
print("---------------------------------------------")
print("order %d" % order)
print("---------------------------------------------")
print("#elements=", len(mesh.elements))
# limiter setup -------------------------------------------------------
from grudge.models.gas_dynamics import SlopeLimiter1NEuler
limiter = SlopeLimiter1NEuler(discr, gamma, 2, op)
# time stepper --------------------------------------------------------
from grudge.timestep import SSPRK3TimeStepper, RK4TimeStepper
#stepper = SSPRK3TimeStepper(limiter=limiter)
#stepper = SSPRK3TimeStepper()
stepper = RK4TimeStepper()
# diagnostics setup ---------------------------------------------------
from pytools.log import LogManager, add_general_quantities, \
add_simulation_quantities, add_run_info
if write_output:
log_file_name = "euler-%d.dat" % order
else:
log_file_name = None
logmgr = LogManager(log_file_name, "w", rcon.communicator)
add_run_info(logmgr)
add_general_quantities(logmgr)
add_simulation_quantities(logmgr)
discr.add_instrumentation(logmgr)
stepper.add_instrumentation(logmgr)
logmgr.add_watches(["step.max", "t_sim.max", "t_step.max"])
# timestep loop -------------------------------------------------------
t = 0
#fields = limiter(fields)
try:
from grudge.timestep import times_and_steps
step_it = times_and_steps(
final_time=.1,
#max_steps=500,
logmgr=logmgr,
max_dt_getter=lambda t: 0.4*op.estimate_timestep(discr,
stepper=stepper, t=t, max_eigenvalue=max_eigval[0]))
for step, t, dt in step_it:
if step % 1 == 0 and write_output:
#if False:
visf = vis.make_file("vortex-%d-%04d" % (order, step))
true_fields = vortex.volume_interpolant(t, discr)
#rhs_fields = rhs(t, fields)
from pyvisfile.silo import DB_VARTYPE_VECTOR
vis.add_data(visf,
[
("rho", discr.convert_volume(op.rho(fields), kind="numpy")),
("e", discr.convert_volume(op.e(fields), kind="numpy")),
("rho_u", discr.convert_volume(op.rho_u(fields), kind="numpy")),
("u", discr.convert_volume(op.u(fields), kind="numpy")),
#("true_rho", discr.convert_volume(op.rho(true_fields), kind="numpy")),
#("true_e", discr.convert_volume(op.e(true_fields), kind="numpy")),
#("true_rho_u", discr.convert_volume(op.rho_u(true_fields), kind="numpy")),
#("true_u", discr.convert_volume(op.u(true_fields), kind="numpy")),
#("rhs_rho", discr.convert_volume(op.rho(rhs_fields), kind="numpy")),
#("rhs_e", discr.convert_volume(op.e(rhs_fields), kind="numpy")),
#("rhs_rho_u", discr.convert_volume(op.rho_u(rhs_fields), kind="numpy")),
],
expressions=[
#("diff_rho", "rho-true_rho"),
#("diff_e", "e-true_e"),
#("diff_rho_u", "rho_u-true_rho_u", DB_VARTYPE_VECTOR),
("p", "0.4*(e- 0.5*(rho_u*u))"),
],
time=t, step=step
)
visf.close()
fields = stepper(fields, t, dt, rhs)
true_fields = vortex.volume_interpolant(t, discr)
l2_error = discr.norm(fields-true_fields)
l2_error_rho = discr.norm(op.rho(fields)-op.rho(true_fields))
l2_error_e = discr.norm(op.e(fields)-op.e(true_fields))
l2_error_rhou = discr.norm(op.rho_u(fields)-op.rho_u(true_fields))
l2_error_u = discr.norm(op.u(fields)-op.u(true_fields))
eoc_rec.add_data_point(order, l2_error_rho)
print()
print(eoc_rec.pretty_print("P.Deg.", "L2 Error"))
logmgr.set_constant("l2_error", l2_error)
logmgr.set_constant("l2_error_rho", l2_error_rho)
logmgr.set_constant("l2_error_e", l2_error_e)
logmgr.set_constant("l2_error_rhou", l2_error_rhou)
logmgr.set_constant("l2_error_u", l2_error_u)
logmgr.set_constant("refinement", refine)
finally:
if write_output:
vis.close()
logmgr.close()
discr.close()
# after order loop
#assert eoc_rec.estimate_order_of_convergence()[0,1] > 6
if __name__ == "__main__":
main()
# entry points for py.test ----------------------------------------------------
from pytools.test import mark_test
@mark_test.long
def test_euler_vortex():
main(write_output=False)