def fig_61_62_63(kernel_language='Python',
iplot=False,
htmlplot=False,
solver_type='classic',
outdir='./_output'):
"""
Compare several methods for advecting a Gaussian and square wave.
The settings coded here are for Figure 6.1(a).
For Figure 6.1(b), set solver.order=2.
For Figure 6.2(a), set solver.order=2 and solver.limiters = pyclaw.limiters.tvd.minmod
For Figure 6.2(b), set solver.order=2 and solver.limiters = pyclaw.limiters.tvd.superbee
For Figure 6.2(c), set solver.order=2 and solver.limiters = pyclaw.limiters.tvd.MC
For Figure 6.3, set IC='wavepacket' and other options as appropriate.
"""
import numpy as np
from clawpack import pyclaw
if solver_type == 'sharpclaw':
solver = pyclaw.SharpClawSolver1D()
else:
solver = pyclaw.ClawSolver1D()
solver.kernel_language = kernel_language
from clawpack.riemann import rp_advection
solver.num_waves = rp_advection.num_waves
if solver.kernel_language == 'Python':
solver.rp = rp_advection.rp_advection_1d
solver.bc_lower[0] = 2
solver.bc_upper[0] = 2
solver.limiters = 0
solver.order = 1
solver.cfl_desired = 0.8
x = pyclaw.Dimension('x', 0.0, 1.0, mx)
grid = pyclaw.Grid(x)
num_eqn = 1
state = pyclaw.State(grid, num_eqn)
state.problem_data['u'] = 1.
xc = grid.x.center
if IC == 'gauss_square':
state.q[0, :] = np.exp(-beta * (xc - x0)**2) + (xc > 0.6) * (xc < 0.8)
elif IC == 'wavepacket':
state.q[0, :] = np.exp(-beta * (xc - x0)**2) * np.sin(80. * xc)
else:
raise Exception('Unrecognized initial condition specification.')
claw = pyclaw.Controller()
claw.solution = pyclaw.Solution(state)
claw.solver = solver
claw.outdir = outdir
claw.tfinal = 10.0
status = claw.run()
if htmlplot: pyclaw.plot.html_plot(outdir=outdir)
if iplot: pyclaw.plot.interactive_plot(outdir=outdir)
def advect_1d(u, qfunc, qkws={},
nx=200, dx=500.,
t_out=np.arange(0, 3601, 5*60),
sharp=True):
""" Run a 1D advection calculation via clawpack. CONSTANT U ONLY.
"""
rp = riemann.advection_1D
if sharp:
solver = pyclaw.SharpClawSolver1D(rp)
solver.weno_order = 5
else:
solver = pyclaw.ClawSolver1D(rp)
solver.bc_lower[0] = pyclaw.BC.periodic
solver.bc_upper[0] = pyclaw.BC.periodic
x = pyclaw.Dimension(0, dx*nx, nx, name='x')
domain = pyclaw.Domain(x)
state = pyclaw.State(domain, solver.num_eqn)
state.problem_data['u'] = u
x1d = domain.grid.x.centers
q = qfunc(x1d, t=0)
state.q[0, ...] = q
claw = pyclaw.Controller()
claw.keep_copy = True
claw.solution = pyclaw.Solution(state, domain)
claw.solver = solver
claw.tfinal = t_out[-1]
claw.out_times = t_out
claw.num_output_times = len(t_out) - 1
claw.run()
times = claw.out_times
tracers = [f.q.squeeze() for f in claw.frames]
tracers = np.asarray(tracers)
uarr = u*np.ones_like(x1d)
ds = xr.Dataset(
{'q': (('time', 'x'), tracers),
'u': (('x', ), uarr)},
{'time': times, 'x': x1d}
)
ds['time'].attrs.update({'long_name': 'time', 'units': 'seconds since 2000-01-01 0:0:0'})
ds['x'].attrs.update({'long_name': 'x-coordinate', 'units': 'm'})
ds['u'].attrs.update({'long_name': 'zonal wind', 'units': 'm/s'})
ds.attrs.update({
'Conventions': 'CF-1.7'
})
return ds
def advection_setup(nx=100,
solver_type='classic',
lim_type=2,
weno_order=5,
CFL=0.9,
time_integrator='SSP104',
outdir='./_output'):
riemann_solver = riemann.advection_1D
if solver_type == 'classic':
solver = pyclaw.ClawSolver1D(riemann_solver)
elif solver_type == 'sharpclaw':
solver = pyclaw.SharpClawSolver1D(riemann_solver)
solver.lim_type = lim_type
solver.weno_order = weno_order
solver.time_integrator = time_integrator
else:
raise Exception('Unrecognized value of solver_type.')
solver.kernel_language = 'Fortran'
solver.cfl_desired = CFL
solver.cfl_max = CFL * 1.1
solver.bc_lower[0] = pyclaw.BC.periodic
solver.bc_upper[0] = pyclaw.BC.periodic
x = pyclaw.Dimension(0.0, 1.0, nx, name='x')
domain = pyclaw.Domain(x)
state = pyclaw.State(domain, solver.num_eqn)
state.problem_data['u'] = 1. # Advection velocity
# Initial data
xc = state.grid.x.centers
beta = 100
gamma = 0
x0 = 0.75
state.q[0, :] = np.exp(-beta * (xc - x0)**2) * np.cos(gamma * (xc - x0))
claw = pyclaw.Controller()
claw.keep_copy = True
claw.solution = pyclaw.Solution(state, domain)
claw.solver = solver
if outdir is not None:
claw.outdir = outdir
else:
claw.output_format = None
claw.tfinal = 1.0
return claw
def __init__(self, cparams, dtype_u, dtype_f):
"""
Initialization routine
Args:
cparams: custom parameters for the example
dtype_u: particle data type (will be passed parent class)
dtype_f: acceleration data type (will be passed parent class)
"""
# these parameters will be used later, so assert their existence
assert 'nvars' in cparams
assert 'dt' in cparams
# add parameters as attributes for further reference
for k, v in cparams.items():
setattr(self, k, v)
# invoke super init, passing number of dofs, dtype_u and dtype_f
super(sharpclaw, self).__init__(self.nvars, dtype_u, dtype_f)
riemann_solver = riemann.advection_1D # NOTE: This uses the FORTRAN kernels of clawpack
self.solver = pyclaw.SharpClawSolver1D(riemann_solver)
self.solver.weno_order = 5
self.solver.time_integrator = 'Euler' # Remove later
self.solver.kernel_language = 'Fortran'
self.solver.bc_lower[0] = pyclaw.BC.periodic
self.solver.bc_upper[0] = pyclaw.BC.periodic
self.solver.cfl_max = 1.0
assert self.solver.is_valid()
x = pyclaw.Dimension(0.0, 1.0, self.nvars, name='x')
self.domain = pyclaw.Domain(x)
self.state = pyclaw.State(self.domain, self.solver.num_eqn)
self.state.problem_data['u'] = 1.0
self.dx = self.state.grid.x.centers[1] - self.state.grid.x.centers[0]
# Initial data
u0 = self.u_exact(0.0)
self.state.q[0, :] = u0.values
solution = pyclaw.Solution(self.state, self.domain)
self.solver.setup(solution)
def __init__(self,
domain_config,
solver_type="sharpclaw",
kernel_language="Python"):
tau = domain_config["tau"]
if kernel_language == "Python":
rs = riemann.euler_1D_py.euler_hllc_1D
elif kernel_language == "Fortran":
rs = riemann.euler_with_efix_1D
if solver_type == "sharpclaw":
solver = pyclaw.SharpClawSolver1D(rs)
solver.dq_src = lambda x, y, z: dq_src(x, y, z, tau)
elif solver_type == "classic":
solver = pyclaw.ClawSolver1D(rs)
solver.step_source = lambda x, y, z: q_src(x, y, z, tau)
solver.kernel_language = kernel_language
solver.bc_lower[0] = pyclaw.BC.periodic
solver.bc_upper[0] = pyclaw.BC.periodic
nx = domain_config["nx"]
xmin, xmax = domain_config["xmin"], domain_config["xmax"]
x = pyclaw.Dimension(xmin, xmax, nx, name="x")
domain = pyclaw.Domain([x])
state = pyclaw.State(domain, num_eqn)
state.problem_data["gamma"] = gamma
state.problem_data["gamma1"] = gamma - 1.0
solution = pyclaw.Solution(state, domain)
claw = pyclaw.Controller()
claw.solution = solution
claw.solver = solver
self._solver = solver
self._domain = domain
self._solution = solution
self._claw = claw
def stegoton(rkm, tol, iplot=0, htmlplot=0, outdir='./_output'):
"""
Stegoton problem.
Nonlinear elasticity in periodic medium.
See LeVeque & Yong (2003).
$$\\epsilon_t - u_x = 0$$
$$\\rho(x) u_t - \\sigma(\\epsilon,x)_x = 0$$
"""
from clawpack import pyclaw
solver = pyclaw.SharpClawSolver1D()
solver.time_integrator = 'RK'
solver.A = rkm.A
solver.b = rkm.b
solver.b_hat = rkm.bhat
solver.c = rkm.c
solver.error_tolerance = tol
solver.dt_variable = True
solver.cfl_max = 2.5
solver.cfl_desired = 1.5
solver.weno_order = 5
from clawpack import riemann
solver.rp = riemann.rp1_nonlinear_elasticity_fwave
solver.bc_lower[0] = pyclaw.BC.periodic
solver.bc_upper[0] = pyclaw.BC.periodic
#Use the same BCs for the aux array
solver.aux_bc_lower = solver.bc_lower
solver.aux_bc_upper = solver.bc_lower
xlower = 0.0
xupper = 300.0
cellsperlayer = 6
mx = int(round(xupper - xlower)) * cellsperlayer
x = pyclaw.Dimension('x', xlower, xupper, mx)
domain = pyclaw.Domain(x)
num_eqn = 2
state = pyclaw.State(domain, num_eqn)
#Set global parameters
alpha = 0.5
KA = 1.0
KB = 4.0
rhoA = 1.0
rhoB = 4.0
state.problem_data = {}
state.problem_data['t1'] = 10.0
state.problem_data['tw1'] = 10.0
state.problem_data['a1'] = 0.0
state.problem_data['alpha'] = alpha
state.problem_data['KA'] = KA
state.problem_data['KB'] = KB
state.problem_data['rhoA'] = rhoA
state.problem_data['rhoB'] = rhoB
state.problem_data['trtime'] = 25000.0
state.problem_data['trdone'] = False
#Initialize q and aux
xc = state.grid.x.centers
state.aux = setaux(xc,
rhoB,
KB,
rhoA,
KA,
alpha,
xlower=xlower,
xupper=xupper)
a2 = 1.0
sigma = a2 * np.exp(-((xc - xupper / 2.) / 5.)**2.)
state.q[0, :] = np.log(sigma + 1.) / state.aux[1, :]
state.q[1, :] = 0.
tfinal = 100.
num_output_times = 10
solver.max_steps = 5000000
solver.fwave = True
solver.num_waves = 2
solver.lim_type = 2
solver.char_decomp = 0
claw = pyclaw.Controller()
claw.keep_copy = True
claw.output_style = 1
claw.num_output_times = num_output_times
claw.tfinal = tfinal
claw.solution = pyclaw.Solution(state, domain)
claw.solver = solver
# Solve
status = claw.run()
print claw.solver.status['totalsteps']
if htmlplot: pyclaw.plot.html_plot(outdir=outdir)
if iplot: pyclaw.plot.interactive_plot(outdir=outdir)
epsilon = claw.frames[-1].q[0, :]
aux = claw.frames[1].aux
from clawpack.riemann.rp_nonlinear_elasticity import sigma
stress = sigma(epsilon, aux[1, :])
dx = state.grid.delta[0]
work = solver.status['totalsteps']
return stress, dx, work
def fig_31_38(kernel_language='Fortran',
solver_type='classic',
iplot=False,
htmlplot=False,
outdir='./_output'):
r"""Produces the output shown in Figures 3.1 and 3.8 of the FVM book.
These involve simple waves in the acoustics system."""
from clawpack import pyclaw
import numpy as np
#=================================================================
# Import the appropriate solver type, depending on the options passed
#=================================================================
if solver_type == 'classic':
solver = pyclaw.ClawSolver1D()
elif solver_type == 'sharpclaw':
solver = pyclaw.SharpClawSolver1D()
else:
raise Exception('Unrecognized value of solver_type.')
#========================================================================
# Instantiate the solver and define the system of equations to be solved
#========================================================================
solver.kernel_language = kernel_language
from clawpack.riemann import rp_acoustics
solver.num_waves = rp_acoustics.num_waves
if kernel_language == 'Python':
solver.rp = rp_acoustics.rp_acoustics_1d
solver.limiters = pyclaw.limiters.tvd.MC
solver.bc_lower[0] = pyclaw.BC.wall
solver.bc_upper[0] = pyclaw.BC.extrap
#========================================================================
# Instantiate the grid and set the boundary conditions
#========================================================================
x = pyclaw.Dimension('x', -1.0, 1.0, 800)
grid = pyclaw.Grid(x)
num_eqn = 2
state = pyclaw.State(grid, num_eqn)
#========================================================================
# Set problem-specific variables
#========================================================================
rho = 1.0
bulk = 0.25
state.problem_data['rho'] = rho
state.problem_data['bulk'] = bulk
state.problem_data['zz'] = np.sqrt(rho * bulk)
state.problem_data['cc'] = np.sqrt(bulk / rho)
#========================================================================
# Set the initial condition
#========================================================================
xc = grid.x.center
beta = 100
gamma = 0
x0 = 0.75
state.q[0, :] = 0.5 * np.exp(-80 * xc**2) + 0.5 * (np.abs(xc + 0.2) < 0.1)
state.q[1, :] = 0.
#========================================================================
# Set up the controller object
#========================================================================
claw = pyclaw.Controller()
claw.solution = pyclaw.Solution(state)
claw.solver = solver
claw.outdir = outdir
claw.tfinal = 3.0
claw.num_output_times = 30
# Solve
status = claw.run()
# Plot results
if htmlplot: pyclaw.plot.html_plot(outdir=outdir)
if iplot: pyclaw.plot.interactive_plot(outdir=outdir)
def acoustics(solver_type='classic',
iplot=True,
htmlplot=False,
outdir='./_output',
problem='figure 9.4'):
"""
This example solves the 1-dimensional variable-coefficient acoustics
equations in a medium with a single interface.
"""
from numpy import sqrt, abs
from clawpack import pyclaw
if solver_type == 'classic':
solver = pyclaw.ClawSolver1D()
elif solver_type == 'sharpclaw':
solver = pyclaw.SharpClawSolver1D()
else:
raise Exception('Unrecognized value of solver_type.')
solver.num_waves = 2
solver.limiters = pyclaw.limiters.tvd.MC
solver.bc_lower[0] = pyclaw.BC.extrap
solver.bc_upper[0] = pyclaw.BC.extrap
solver.aux_bc_lower[0] = pyclaw.BC.extrap
solver.aux_bc_upper[0] = pyclaw.BC.extrap
x = pyclaw.Dimension('x', -5.0, 5.0, 500)
grid = pyclaw.Grid(x)
num_eqn = 2
num_aux = 2
state = pyclaw.State(grid, num_eqn, num_aux)
if problem == 'figure 9.4':
rhol = 1.0
cl = 1.0
rhor = 2.0
cr = 0.5
elif problem == 'figure 9.5':
rhol = 1.0
cl = 1.0
rhor = 4.0
cr = 0.5
zl = rhol * cl
zr = rhor * cr
xc = grid.x.center
state.aux[0, :] = (xc <= 0) * zl + (xc > 0) * zr # Impedance
state.aux[1, :] = (xc <= 0) * cl + (xc > 0) * cr # Sound speed
# initial condition: half-ellipse
state.q[0, :] = sqrt(abs(1. - (xc + 3.)**2)) * (xc > -4.) * (xc < -2.)
state.q[1, :] = state.q[0, :] + 0.
claw = pyclaw.Controller()
claw.solution = pyclaw.Solution(state)
claw.solver = solver
claw.tfinal = 5.0
claw.num_output_times = 10
# Solve
status = claw.run()
# Plot results
if htmlplot: pyclaw.plot.html_plot(outdir=outdir)
if iplot: pyclaw.plot.interactive_plot(outdir=outdir)
:param p: Pressure
:param lambd: Reaction progression \in [0, 1]
:return:
"""
return np.heaviside(p - p_ign, 1) * k * (p/p_cj)**mu * (1 - lambd)**upsilon
## PDE equations
# Solvers
"""Solver"""
from clawpack import pyclaw
from clawpack import riemann
rs = riemann.euler_1D_py.euler_hllc_1D
solver = pyclaw.SharpClawSolver1D(rs)
solver.kernel_language = 'Python'
# Boundary conditions
solver.bc_lower[0] = pyclaw.BC.extrap #.wall # Wall in left
solver.bc_upper[0] = pyclaw.BC.extrap # non-wall (zero-order extrapolation) condition at the right boundary
# Domain
mx = 800
x = pyclaw.Dimension(0.0, 0.1, mx, name='x')
print(x)
domain = pyclaw.Domain([x])
# Solution container
solution = pyclaw.Solution(solver.num_eqn, domain)
def setup(use_petsc=False, outdir='./_output', solver_type='classic'):
from clawpack import pyclaw
import euler_roe_1D
import euler_efix_roe_1D
if use_petsc:
import clawpack.petclaw as pyclaw
else:
from clawpack import pyclaw
if solver_type=='sharpclaw':
solver = pyclaw.SharpClawSolver1D(riemann.euler_with_efix_1D)
solver.weno_order = 5
#solver.lim_type = 2
solver.char_decomp = 1
solver.time_integrator = 'SSP104'
else:
#solver = pyclaw.ClawSolver1D(euler_roe_1D)
solver = pyclaw.ClawSolver1D(euler_efix_roe_1D)
solver.bc_lower[0]=pyclaw.BC.extrap
solver.bc_upper[0]=pyclaw.BC.extrap
solver.order = 1
solver.limiters = 1
solver.num_waves = 3
solver.num_eqn = 3
# Initialize domain
mx=400;
x = pyclaw.Dimension('x',0.0,4.0,mx)
domain = pyclaw.Domain([x])
num_eqn = 3
state = pyclaw.State(domain,num_eqn)
state.problem_data['gamma']= gamma
state.problem_data['gamma1']= gamma1
rhol = 1.
rhor = 0.125
ul = 0.5
ur = 0.5
pl = 1.
pr = 0.1
xs1 = -1.
xs2 = 1.25
x =state.grid.x.centers
state.q[0,:] = (x>xs1)*(x<xs2)*rhol + ~((x>xs1)*(x<xs2))*rhor
state.q[1,:] = (x>xs1)*(x<xs2)*rhol*ul + ~((x>xs1)*(x<xs2))*rhor*ur
state.q[2,:] = ((x>xs1)*(x<xs2)*(pl/gamma1 + rhol*ul**2/2) +
~((x>xs1)*(x<xs2))*(pr/gamma1 + rhor*ur**2/2) )
# rhol = 1.
# rhor = 0.125
# ul = 0.
# ur = 0.
# pl = 1.
# pr = 0.1
# xs = 0.5
#
# x =state.grid.x.centers
# state.q[0,:] = (x<xs)*rhol + (x>=xs)*rhor
# state.q[1,:] = (x<xs)*rhol*ul + (x>=xs)*rhor*ur
# state.q[2,:] = (x<xs)*(pl/gamma1 + rhol*ul**2/2) + (x>=xs)*(pr/gamma1 + rhor*ur**2/2)
##
claw = pyclaw.Controller()
claw.tfinal = 2.
claw.solution = pyclaw.Solution(state,domain)
claw.solver = solver
claw.num_output_times = 10
claw.outdir = outdir
claw.setplot = setplot
claw.keep_copy = True
#state.mp = 1
#claw.compute_p = pressure
#claw.write_aux_always = 'True'
return claw
def setup(use_petsc=False,
iplot=False,
htmlplot=False,
outdir='./_output',
solver_type='sharpclaw',
kernel_language='Fortran',
use_char_decomp=False,
tfluct_solver=True):
if use_petsc:
import clawpack.petclaw as pyclaw
else:
from clawpack import pyclaw
if kernel_language == 'Python':
rs = riemann.euler_1D_py.euler_roe_1D
elif kernel_language == 'Fortran':
rs = riemann.euler_with_efix_1D
if solver_type == 'sharpclaw':
solver = pyclaw.SharpClawSolver1D(rs)
solver.time_integrator = 'RK'
solver.a, solver.b, solver.c = a, b, c
solver.cfl_desired = 0.6
solver.cfl_max = 0.7
if use_char_decomp:
try:
from . import sharpclaw1 # Import custom Fortran code
solver.fmod = sharpclaw1
solver.tfluct_solver = tfluct_solver # Use total fluctuation solver for efficiency
if solver.tfluct_solver:
try:
from . import euler_tfluct
solver.tfluct = euler_tfluct
except ImportError:
import logging
logger = logging.getLogger()
logger.error(
'Unable to load tfluct solver, did you run make?')
print(
'Unable to load tfluct solver, did you run make?')
raise
except ImportError:
import logging
logger = logging.getLogger()
logger.error(
'Unable to load sharpclaw1 solver, did you run make?')
print('Unable to load sharpclaw1 solver, did you run make?')
pass
solver.lim_type = 2 # WENO reconstruction
solver.char_decomp = 2 # characteristic-wise reconstruction
else:
solver = pyclaw.ClawSolver1D(rs)
solver.kernel_language = kernel_language
solver.bc_lower[0] = pyclaw.BC.extrap
solver.bc_upper[0] = pyclaw.BC.extrap
mx = 400
x = pyclaw.Dimension(-5.0, 5.0, mx, name='x')
domain = pyclaw.Domain([x])
state = pyclaw.State(domain, num_eqn)
state.problem_data['gamma'] = gamma
if kernel_language == 'Python':
state.problem_data['efix'] = False
xc = state.grid.p_centers[0]
epsilon = 0.2
velocity = (xc < -4.) * 2.629369
pressure = (xc < -4.) * 10.33333 + (xc >= -4.) * 1.
state.q[density, :] = (xc < -4.) * 3.857143 + (xc >= -4.) * (
1 + epsilon * np.sin(5 * xc))
state.q[momentum, :] = velocity * state.q[density, :]
state.q[energy, :] = pressure / (
gamma - 1.) + 0.5 * state.q[density, :] * velocity**2
claw = pyclaw.Controller()
claw.tfinal = 1.8
claw.solution = pyclaw.Solution(state, domain)
claw.solver = solver
claw.num_output_times = 10
claw.outdir = outdir
claw.setplot = setplot
claw.keep_copy = True
return claw
