def kpp(use_petsc=False,
iplot=False,
htmlplot=False,
outdir='./_output',
solver_type='classic'):
"""
Example python script for solving the 2d KPP equations.
"""
if use_petsc:
import petclaw as pyclaw
else:
import pyclaw
if solver_type == 'sharpclaw':
solver = pyclaw.SharpClawSolver2D()
else:
solver = pyclaw.ClawSolver2D()
import riemann
solver.rp = riemann.rp2_kpp
solver.num_waves = 1
solver.bc_lower[0] = pyclaw.BC.extrap
solver.bc_upper[0] = pyclaw.BC.extrap
solver.bc_lower[1] = pyclaw.BC.extrap
solver.bc_upper[1] = pyclaw.BC.extrap
# Initialize domain
mx = 200
my = 200
x = pyclaw.Dimension('x', -2.0, 2.0, mx)
y = pyclaw.Dimension('y', -2.0, 2.0, my)
domain = pyclaw.Domain([x, y])
num_eqn = 1
state = pyclaw.State(domain, num_eqn)
qinit(state)
solver.dimensional_split = 1
solver.cfl_max = 1.0
solver.cfl_desired = 0.9
solver.num_waves = 2
solver.limiters = pyclaw.limiters.tvd.minmod
claw = pyclaw.Controller()
claw.tfinal = 1.0
claw.solution = pyclaw.Solution(state, domain)
claw.solver = solver
claw.num_output_times = 10
# Solve
status = claw.run()
if htmlplot: pyclaw.plot.html_plot(outdir=outdir)
if iplot: pyclaw.plot.interactive_plot(outdir=outdir)
def advection2D(iplot=False,
use_petsc=False,
htmlplot=False,
outdir='./_output',
solver_type='classic'):
"""
Example python script for solving the 2d advection equation.
"""
#===========================================================================
# Import libraries
#===========================================================================
if use_petsc:
import petclaw as pyclaw
else:
import pyclaw
#===========================================================================
# Setup solver and solver parameters
#===========================================================================
if solver_type == 'classic':
solver = pyclaw.ClawSolver2D()
solver.dimensional_split = 1
solver.limiters = pyclaw.limiters.tvd.vanleer
elif solver_type == 'sharpclaw':
solver = pyclaw.SharpClawSolver2D()
import riemann
solver.rp = riemann.rp2_advection
solver.bc_lower[0] = pyclaw.BC.periodic
solver.bc_upper[0] = pyclaw.BC.periodic
solver.bc_lower[1] = pyclaw.BC.periodic
solver.bc_upper[1] = pyclaw.BC.periodic
solver.num_waves = 1
solver.cfl_max = 1.0
solver.cfl_desired = 0.9
#===========================================================================
# Initialize domain, then initialize the solution associated to the domain and
# finally initialize aux array
#===========================================================================
# Domain:
mx = 50
my = 50
x = pyclaw.Dimension('x', 0.0, 1.0, mx)
y = pyclaw.Dimension('y', 0.0, 1.0, my)
domain = pyclaw.Domain([x, y])
num_eqn = 1
state = pyclaw.State(domain, num_eqn)
state.problem_data['u'] = 0.5 # Parameters (global auxiliary variables)
state.problem_data['v'] = 1.0
# Initial solution
# ================
qinit(state) # This function is defined above
#===========================================================================
# Set up controller and controller parameters
#===========================================================================
claw = pyclaw.Controller()
claw.tfinal = 2.0
claw.solution = pyclaw.Solution(state, domain)
claw.solver = solver
claw.outdir = outdir
#===========================================================================
# Solve the problem
#===========================================================================
status = claw.run()
#===========================================================================
# Plot results
#===========================================================================
if htmlplot: pyclaw.plot.html_plot(outdir=outdir)
if iplot: pyclaw.plot.interactive_plot(outdir=outdir)
def acoustics2D(use_petsc=False,
kernel_language='Fortran',
iplot=False,
htmlplot=False,
solver_type='classic',
outdir='./_output',
num_output_times=10):
"""
Example python script for solving the 2d acoustics equations.
"""
if use_petsc:
import petclaw as pyclaw
else:
import pyclaw
if solver_type == 'classic':
solver = pyclaw.ClawSolver2D()
solver.dimensional_split = 1
solver.num_waves = 2
solver.limiters = [4] * solver.num_waves
elif solver_type == 'sharpclaw':
solver = pyclaw.SharpClawSolver2D()
solver.num_waves = 2
solver.cfl_max = 0.5
solver.cfl_desired = 0.45
solver.bc_lower[0] = pyclaw.BC.extrap
solver.bc_upper[0] = pyclaw.BC.extrap
solver.bc_lower[1] = pyclaw.BC.extrap
solver.bc_upper[1] = pyclaw.BC.extrap
# Initialize domain
mx = 100
my = 100
x = pyclaw.Dimension('x', -1.0, 1.0, mx)
y = pyclaw.Dimension('y', -1.0, 1.0, my)
domain = pyclaw.Domain([x, y])
num_eqn = 3
state = pyclaw.State(domain, num_eqn)
rho = 1.0
bulk = 4.0
cc = np.sqrt(bulk / rho)
zz = rho * cc
state.problem_data['rho'] = rho
state.problem_data['bulk'] = bulk
state.problem_data['zz'] = zz
state.problem_data['cc'] = cc
tfinal = 0.12
qinit(state)
initial_solution = pyclaw.Solution(state, domain)
solver.dt_initial = np.min(
domain.delta) / state.problem_data['cc'] * solver.cfl_desired
claw = pyclaw.Controller()
claw.keep_copy = True
# The output format MUST be set to petsc!
claw.tfinal = tfinal
claw.solution = initial_solution
claw.solver = solver
claw.outdir = outdir
claw.num_output_times = num_output_times
# Solve
status = claw.run()
if htmlplot: pyclaw.plot.html_plot()
if iplot: pyclaw.plot.interactive_plot()
if use_petsc:
grid = domain.grid
pressure = claw.frames[
claw.num_output_times].state.gqVec.getArray().reshape(
[state.num_eqn, grid.num_cells[0], grid.num_cells[1]],
order='F')[0, :, :]
else:
pressure = claw.frames[claw.num_output_times].state.q[0, :, :]
return pressure
def acoustics2D(iplot=False,
htmlplot=False,
use_petsc=False,
outdir='./_output',
solver_type='classic'):
"""
Example python script for solving the 2d acoustics equations.
"""
if use_petsc:
import petclaw as pyclaw
else:
import pyclaw
if solver_type == 'classic':
solver = pyclaw.ClawSolver2D()
solver.dimensional_split = False
elif solver_type == 'sharpclaw':
solver = pyclaw.SharpClawSolver2D()
solver.num_waves = 2
solver.limiters = pyclaw.limiters.tvd.MC
solver.bc_lower[0] = pyclaw.BC.wall
solver.bc_upper[0] = pyclaw.BC.extrap
solver.bc_lower[1] = pyclaw.BC.wall
solver.bc_upper[1] = pyclaw.BC.extrap
# Initialize domain
mx = 100
my = 100
x = pyclaw.Dimension('x', -1.0, 1.0, mx)
y = pyclaw.Dimension('y', -1.0, 1.0, my)
domain = pyclaw.Domain([x, y])
num_eqn = 3
state = pyclaw.State(domain, num_eqn)
rho = 1.0
bulk = 4.0
cc = np.sqrt(bulk / rho)
zz = rho * cc
state.problem_data['rho'] = rho
state.problem_data['bulk'] = bulk
state.problem_data['zz'] = zz
state.problem_data['cc'] = cc
grid = state.grid
Y, X = np.meshgrid(grid.y.centers, grid.x.centers)
r = np.sqrt(X**2 + Y**2)
width = 0.2
state.q[0, :, :] = (np.abs(r - 0.5) <= width) * (1. +
np.cos(np.pi *
(r - 0.5) / width))
state.q[1, :, :] = 0.
state.q[2, :, :] = 0.
claw = pyclaw.Controller()
claw.keep_copy = True
claw.solution = pyclaw.Solution(state, domain)
claw.solver = solver
claw.outdir = outdir
# Solve
claw.tfinal = 0.6
status = claw.run()
if htmlplot:
pyclaw.plot.html_plot(outdir=outdir, file_format=claw.output_format)
if iplot:
pyclaw.plot.interactive_plot(outdir=outdir,
file_format=claw.output_format)
if use_petsc:
pressure = claw.frames[
claw.num_output_times].state.gqVec.getArray().reshape(
[grid.num_cells[0], grid.num_cells[1], state.num_eqn])[:, :, 0]
else:
pressure = claw.frames[claw.num_output_times].state.q[:, :, 0]
return pressure
def shockbubble(use_petsc=False,
iplot=False,
htmlplot=False,
outdir='./_output',
solver_type='classic'):
"""
Solve the Euler equations of compressible fluid dynamics.
This example involves a bubble of dense gas that is impacted by a shock.
"""
if use_petsc:
import petclaw as pyclaw
else:
import pyclaw
if solver_type == 'sharpclaw':
solver = pyclaw.SharpClawSolver2D()
solver.dq_src = dq_Euler_radial
solver.weno_order = 5
solver.lim_type = 2
else:
solver = pyclaw.ClawSolver2D()
solver.dimensional_split = 0
solver.transverse_waves = 2
solver.limiters = [4, 4, 4, 4, 2]
solver.step_source = step_Euler_radial
solver.num_waves = 5
solver.bc_lower[0] = pyclaw.BC.custom
solver.bc_upper[0] = pyclaw.BC.extrap
solver.bc_lower[1] = pyclaw.BC.wall
solver.bc_upper[1] = pyclaw.BC.extrap
#Aux variable in ghost cells doesn't matter
solver.aux_bc_lower[0] = pyclaw.BC.extrap
solver.aux_bc_upper[0] = pyclaw.BC.extrap
solver.aux_bc_lower[1] = pyclaw.BC.extrap
solver.aux_bc_upper[1] = pyclaw.BC.extrap
# Initialize domain
mx = 160
my = 40
x = pyclaw.Dimension('x', 0.0, 2.0, mx)
y = pyclaw.Dimension('y', 0.0, 0.5, my)
domain = pyclaw.Domain([x, y])
num_eqn = 5
num_aux = 1
state = pyclaw.State(domain, num_eqn, num_aux)
state.problem_data['gamma'] = gamma
state.problem_data['gamma1'] = gamma1
qinit(state)
auxinit(state)
solver.user_bc_lower = shockbc
claw = pyclaw.Controller()
claw.tfinal = 0.75
claw.solution = pyclaw.Solution(state, domain)
claw.solver = solver
claw.num_output_times = 10
claw.outdir = outdir
# Solve
status = claw.run()
if htmlplot: pyclaw.plot.html_plot(outdir=outdir)
if iplot: pyclaw.plot.interactive_plot(outdir=outdir)
return claw.solution.q
def shockbubble(use_petsc=False,iplot=False,htmlplot=False,outdir='./_output',solver_type='classic'):
"""
Solve the Euler equations of compressible fluid dynamics.
This example involves a bubble of dense gas that is impacted by a shock.
"""
if use_petsc:
import petclaw as pyclaw
else:
import pyclaw
if solver_type=='sharpclaw':
solver = pyclaw.SharpClawSolver2D()
solver.dq_src=dq_Euler_radial
else:
solver = pyclaw.ClawSolver2D()
solver.dim_split = 0
solver.order_trans = 2
solver.limiters = [4,4,4,4,2]
solver.step_src=step_Euler_radial
solver.mwaves = 5
solver.bc_lower[0]=pyclaw.BC.custom
solver.bc_upper[0]=pyclaw.BC.outflow
solver.bc_lower[1]=pyclaw.BC.reflecting
solver.bc_upper[1]=pyclaw.BC.outflow
#Aux variable in ghost cells doesn't matter
solver.aux_bc_lower[0]=pyclaw.BC.outflow
solver.aux_bc_upper[0]=pyclaw.BC.outflow
solver.aux_bc_lower[1]=pyclaw.BC.outflow
solver.aux_bc_upper[1]=pyclaw.BC.outflow
# Initialize grid
mx=320; my=80
x = pyclaw.Dimension('x',0.0,2.0,mx)
y = pyclaw.Dimension('y',0.0,0.5,my)
grid = pyclaw.Grid([x,y])
meqn = 5
maux=8
state = pyclaw.State(grid,meqn,maux)
state.aux_global['gamma']= gamma
state.aux_global['gamma1']= gamma1
qinit(state)
auxinit(state)
solver.user_bc_lower=shockbc
claw = pyclaw.Controller()
claw.tfinal = 0.75
claw.solution = pyclaw.Solution(state)
claw.solver = solver
claw.nout = 10
claw.outdir = outdir
# Solve
status = claw.run()
if htmlplot: pyclaw.plot.html_plot(outdir=outdir)
if iplot: pyclaw.plot.interactive_plot(outdir=outdir)
return claw.solution.q
def shallow2D(use_petsc=False,
iplot=0,
htmlplot=False,
outdir='./_output',
solver_type='classic'):
#===========================================================================
# Import libraries
#===========================================================================
import numpy as np
if use_petsc:
import petclaw as pyclaw
else:
import pyclaw
#===========================================================================
# Setup solver and solver parameters
#===========================================================================
if solver_type == 'classic':
solver = pyclaw.ClawSolver2D()
elif solver_type == 'sharpclaw':
solver = pyclaw.SharpClawSolver2D()
solver.num_waves = 3
solver.limiters = pyclaw.limiters.tvd.MC
solver.bc_lower[0] = pyclaw.BC.extrap
solver.bc_upper[0] = pyclaw.BC.wall
solver.bc_lower[1] = pyclaw.BC.extrap
solver.bc_upper[1] = pyclaw.BC.wall
solver.dimensional_split = 1
#===========================================================================
# Initialize domain and state, then initialize the solution associated to the
# state and finally initialize aux array
#===========================================================================
# Domain:
xlower = -2.5
xupper = 2.5
mx = 150
ylower = -2.5
yupper = 2.5
my = 150
x = pyclaw.Dimension('x', xlower, xupper, mx)
y = pyclaw.Dimension('y', ylower, yupper, my)
domain = pyclaw.Domain([x, y])
num_eqn = 3 # Number of equations
state = pyclaw.State(domain, num_eqn)
grav = 1.0 # Parameter (global auxiliary variable)
state.problem_data['grav'] = grav
# Initial solution
# ================
# Riemann states of the dam break problem
damRadius = 0.5
hl = 2.
ul = 0.
vl = 0.
hr = 1.
ur = 0.
vr = 0.
qinit(state, hl, ul, vl, hr, ur, vl,
damRadius) # This function is defined above
#===========================================================================
# Set up controller and controller parameters
#===========================================================================
claw = pyclaw.Controller()
claw.tfinal = 2.5
claw.solution = pyclaw.Solution(state, domain)
claw.solver = solver
claw.outdir = outdir
claw.num_output_times = 10
#===========================================================================
# Solve the problem
#===========================================================================
status = claw.run()
#===========================================================================
# Plot results
#===========================================================================
if iplot: plot.interactive_plot(outdir=outdir, format=claw.output_format)
if htmlplot: plot.html_plot(outdir=outdir, format=claw.output_format)
def advection_annulus(use_petsc=False,
iplot=0,
htmlplot=False,
outdir='./_output',
solver_type='classic'):
#===========================================================================
# Import libraries
#===========================================================================
if use_petsc:
import petclaw as pyclaw
else:
import pyclaw
#===========================================================================
# Setup solver and solver parameters
#===========================================================================
if solver_type == 'classic':
solver = pyclaw.ClawSolver2D()
elif solver_type == 'sharpclaw':
solver = pyclaw.SharpClawSolver2D()
solver.bc_lower[0] = pyclaw.BC.extrap
solver.bc_upper[0] = pyclaw.BC.extrap
solver.bc_lower[1] = pyclaw.BC.periodic
solver.bc_upper[1] = pyclaw.BC.periodic
solver.aux_bc_lower[0] = pyclaw.BC.custom
solver.aux_bc_upper[0] = pyclaw.BC.custom
solver.user_aux_bc_lower = velocities_lower
solver.user_aux_bc_upper = velocities_upper
solver.aux_bc_lower[1] = pyclaw.BC.periodic
solver.aux_bc_upper[1] = pyclaw.BC.periodic
solver.num_waves = 1
solver.dimensional_split = 0
solver.transverse_waves = 2
solver.order = 2
solver.dt_initial = 0.1
solver.cfl_max = 0.5
solver.cfl_desired = 0.2
solver.limiters = pyclaw.limiters.tvd.vanleer
#===========================================================================
# Initialize domain and state, then initialize the solution associated to the
# state and finally initialize aux array
#===========================================================================
# Domain:
xlower = 0.2
xupper = 1.0
mx = 40
ylower = 0.0
yupper = np.pi * 2.0
my = 120
x = pyclaw.Dimension('x', xlower, xupper, mx)
y = pyclaw.Dimension('y', ylower, yupper, my)
domain = pyclaw.Domain([x, y])
domain.grid.mapc2p = mapc2p_annulus # Override default_mapc2p function implemented in geometry.py
# State:
num_eqn = 1 # Number of equations
state = pyclaw.State(domain, num_eqn)
# Set initial solution
# ====================
qinit(state, mx, my) # This function is defined above
# Set auxiliary array
# ===================
state.aux = setaux(state, mx, my) # This function is defined above
state.index_capa = 2
#===========================================================================
# Set up controller and controller parameters
#===========================================================================
claw = pyclaw.Controller()
claw.keep_copy = False
claw.output_style = 1
claw.num_output_times = 10
claw.tfinal = 1.0
claw.solution = pyclaw.Solution(state, domain)
claw.solver = solver
claw.outdir = outdir
#===========================================================================
# Solve the problem
#===========================================================================
status = claw.run()
#===========================================================================
# Plot results
#===========================================================================
if htmlplot: pyclaw.plot.html_plot(outdir=outdir)
if iplot: pyclaw.plot.interactive_plot(outdir=outdir)
def acoustics2D(iplot=False,
htmlplot=False,
use_petsc=False,
outdir='./_output',
solver_type='classic'):
"""
Example python script for solving the 2d acoustics equations.
"""
if use_petsc:
import petclaw as pyclaw
else:
import pyclaw
if solver_type == 'classic':
solver = pyclaw.ClawSolver2D()
elif solver_type == 'sharpclaw':
solver = pyclaw.SharpClawSolver2D()
solver.dimensional_split = False
solver.num_waves = 2
solver.limiters = pyclaw.limiters.tvd.MC
solver.bc_lower[0] = pyclaw.BC.wall
solver.bc_upper[0] = pyclaw.BC.extrap
solver.bc_lower[1] = pyclaw.BC.wall
solver.bc_upper[1] = pyclaw.BC.extrap
solver.aux_bc_lower[0] = pyclaw.BC.wall
solver.aux_bc_upper[0] = pyclaw.BC.extrap
solver.aux_bc_lower[1] = pyclaw.BC.wall
solver.aux_bc_upper[1] = pyclaw.BC.extrap
# Initialize domain
mx = 200
my = 200
x = pyclaw.Dimension('x', -1.0, 1.0, mx)
y = pyclaw.Dimension('y', -1.0, 1.0, my)
domain = pyclaw.Domain([x, y])
num_eqn = 3
num_aux = 2 # density, sound speed
state = pyclaw.State(domain, num_eqn, num_aux)
# Cell centers coordinates
grid = state.grid
Y, X = np.meshgrid(grid.y.centers, grid.x.centers)
# Set aux arrays
rhol = 4.0
rhor = 1.0
bulkl = 4.0
bulkr = 4.0
cl = np.sqrt(bulkl / rhol)
cr = np.sqrt(bulkr / rhor)
state.aux[0, :, :] = rhol * (X < 0.) + rhor * (X >= 0.) # Density
state.aux[1, :, :] = cl * (X < 0.) + cr * (X >= 0.) # Sound speed
# Set initial condition
x0 = -0.5
y0 = 0.
r = np.sqrt((X - x0)**2 + (Y - y0)**2)
width = 0.1
rad = 0.25
state.q[0, :, :] = (np.abs(r - rad) <= width) * (1. +
np.cos(np.pi *
(r - rad) / width))
state.q[1, :, :] = 0.
state.q[2, :, :] = 0.
claw = pyclaw.Controller()
claw.keep_copy = True
claw.solution = pyclaw.Solution(state, domain)
claw.solver = solver
claw.outdir = outdir
claw.num_output_times = 20
# Solve
claw.tfinal = 0.6
status = claw.run()
if htmlplot:
pyclaw.plot.html_plot(outdir=outdir, file_format=claw.output_format)
if iplot:
pyclaw.plot.interactive_plot(outdir=outdir,
file_format=claw.output_format)
if use_petsc:
pressure = claw.frames[
claw.num_output_times].state.gqVec.getArray().reshape(
[grid.num_cells[0], grid.num_cells[1], state.num_eqn])[:, :, 0]
else:
pressure = claw.frames[claw.num_output_times].state.q[:, :, 0]
return pressure