def stress(current_data):
"""Compute stress from strain and momentum"""
from stegoton import setaux
from clawpack.riemann.rp_nonlinear_elasticity import sigma
aux = setaux(current_data.x)
epsilon = current_data.q[0, :]
stress = sigma(epsilon, aux[1, :])
return stress
def stress(current_data):
"""Compute stress from strain and momentum"""
from stegoton import setaux
from clawpack.riemann.rp_nonlinear_elasticity import sigma
aux=setaux(current_data.x)
epsilon = current_data.q[0,:]
stress = sigma(epsilon,aux[1,:])
return stress
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 / 2.0) / 5.0) ** 2.0)
state.q[0, :] = np.log(sigma + 1.0) / state.aux[1, :]
state.q[1, :] = 0.0
tfinal = 100.0
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 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
