def dam_break_test(plot, show, save):
model = sw.Model()
model.plot = plot
model.show_plot = show
model.save_plot = save
# mesh
model.L_ = 1.0
model.x_N_ = 1.0
# current properties
model.Fr_ = 1.19
model.beta_ = 0.0
# time stepping
model.adapt_timestep = False
model.adapt_initial_timestep = False
model.cfl = Constant(0.5)
# define stabilisation parameters (0.1,0.1,0.1,0.1) found to work well for t=10.0
model.q_b = Constant(0.0)
model.h_b = Constant(0.0)
model.phi_b = Constant(0.0)
model.phi_d_b = Constant(0.0)
# discretisation
model.q_degree = 1
model.h_degree = 1
model.phi_degree = 1
model.phi_d_degree = 1
model.q_disc = "DG"
model.h_disc = "DG"
model.phi_disc = "DG"
model.phi_d_disc = "DG"
model.disc = [model.q_disc, model.h_disc, model.phi_disc, model.phi_d_disc]
def getError(model):
q, h, phi, phi_d, x_N_model, u_N_model = model.w[0].split()
Fq = FunctionSpace(model.mesh, model.q_disc, model.q_degree + 2)
Fh = FunctionSpace(model.mesh, model.h_disc, model.h_degree + 2)
Fphi = FunctionSpace(model.mesh, model.phi_disc, model.phi_degree + 2)
Fphi_d = FunctionSpace(model.mesh, model.phi_d_disc, model.phi_d_degree + 2)
u_N = model.Fr_ / (1.0 + model.Fr_ / 2.0)
h_N = (1.0 / (1.0 + model.Fr_ / 2.0)) ** 2.0
x_N = u_N * model.t
x_M = (2.0 - 3.0 * h_N ** 0.5) * model.t
x_L = -model.t
class u_expression(Expression):
def eval(self, value, x):
x_gate = x[0] * x_N_model - 1.0
if x_gate <= x_L:
value[0] = 0.0
elif x_gate <= x_M:
value[0] = 2.0 / 3.0 * (1.0 + x_gate / model.t)
else:
value[0] = model.Fr_ / (1.0 + model.Fr_ / 2.0)
class h_expression(Expression):
def eval(self, value, x):
x_gate = x[0] * x_N_model - 1.0
if x_gate <= x_L:
value[0] = 1.0
elif x_gate <= x_M:
value[0] = 1.0 / 9.0 * (2.0 - x_gate / model.t) ** 2.0
else:
value[0] = (1.0 / (1.0 + model.Fr_ / 2.0)) ** 2.0
S_q = project(u_expression(), Fq)
S_h = project(h_expression(), Fh)
E_q = errornorm(q, S_q, norm_type="L2", degree_rise=2)
E_h = errornorm(h, S_h, norm_type="L2", degree_rise=2)
E_x_N = abs(x_N_model - x_N)
E_u_N = abs(u_N_model - u_N)
return E_q, E_h, E_x_N, E_u_N
# long test
T = 0.5
dt = [1e-1, 1e-1 / 2, 1e-1 / 4, 1e-1 / 8, 1e-1 / 16, 1e-1 / 32, 1e-1 / 64, 1e-1 / 128, 1e-1 / 256, 1e-1 / 512]
dX = [1.0 / 4, 1.0 / 8, 1.0 / 16, 1.0 / 32, 1.0 / 64]
dt = [1e-1 / 32]
dX = [1.0 / 16, 1.0 / 32, 1.0 / 64]
# quick settings
dt = [1e-1 / 64]
dX = [1.0 / 16, 1.0 / 32, 1.0 / 64]
dX = [1.0 / 64]
E = []
for dt_ in dt:
E.append([])
for dX_ in dX:
print dX_, dt_
model.dX_ = dX_
model.timestep = dt_
model.t = 0.0
model.initialise_function_spaces()
model.setup(zero_q=True, dam_break=True)
model.error_callback = getError
E[-1].append(model.solve(T))
sw_io.write_array_to_file("dam_break.json", E, "w")
E = E[0]
print ("R = 0.00 0.00 0.00 0.00 0.00 E = %.2e %.2e %.2e %.2e %.2e" % (E[0][0], E[0][1], E[0][2], E[0][3]))
for i in range(1, len(E)):
rh = np.log(E[i][0] / E[i - 1][0]) / np.log(dX[i] / dX[i - 1])
rq = np.log(E[i][1] / E[i - 1][1]) / np.log(dX[i] / dX[i - 1])
rx = np.log(E[i][2] / E[i - 1][2]) / np.log(dX[i] / dX[i - 1])
ru = np.log(E[i][3] / E[i - 1][3]) / np.log(dX[i] / dX[i - 1])
print (
"R = %-5.2f %-5.2f %-5.2f %-5.2f %-5.2f E = %.2e %.2e %.2e %.2e %.2e"
% (rh, rq, rx, ru, E[i][0], E[i][1], E[i][2], E[i][3])
)
def __call__(self, value):
try:
print "\n* * * Adjoint and optimiser time taken = {}".format(toc())
list_timings(True)
except:
pass
#### initial condition dump hack ####
phi_ic = value[0].vector().array()
phi = phi_ic.copy()
for i in range(len(model.mesh.cells())):
j = i*2
phi[j] = phi_ic[-(j+2)]
phi[j+1] = phi_ic[-(j+1)]
phi_ic = phi
sw_io.write_array_to_file('phi_ic_adj{}_latest.json'.format(job),phi_ic,'w')
sw_io.write_array_to_file('phi_ic_adj{}.json'.format(job),phi_ic,'a')
try:
h_ic = value[1].vector().array()
sw_io.write_array_to_file('h_ic_adj{}_latest.json'.format(job),h_ic,'w')
sw_io.write_array_to_file('h_ic_adj{}.json'.format(job),h_ic,'a')
except:
pass
try:
q_a_ = value[2]((0,0)); q_pa_ = value[3]((0,0)); q_pb_ = value[4]((0,0))
sw_io.write_q_vals_to_file('q_ic_adj{}_latest.json'.format(job),q_a_,q_pa_,q_pb_,'w')
sw_io.write_q_vals_to_file('q_ic_adj{}.json'.format(job),q_a_,q_pa_,q_pb_,'a')
except:
pass
tic()
print "\n* * * Computing forward model"
func_value = (super(MyReducedFunctional, self)).__call__(value)
# model.setup(h_ic = value[1], phi_ic = value[0], q_a = value[2], q_pa = value[3], q_pb = value[4])
# model.solve(T = options.T)
# func_value = adjointer.evaluate_functional(self.functional, 0)
print "* * * Forward model: time taken = {}".format(toc())
list_timings(True)
# sys.exit()
j = self.scale * func_value
j_log.append(j)
sw_io.write_array_to_file('j_log{}.json'.format(job), j_log, 'w')
(fwd_var, output) = adjointer.get_forward_solution(adjointer.equation_count - 1)
var = adjointer.get_variable_value(fwd_var)
y, q, h, phi, phi_d, x_N, u_N = sw_io.map_to_arrays(var.data, model.y, model.mesh)
sw_io.write_array_to_file('phi_d_adj{}_latest.json'.format(job),phi_d,'w')
sw_io.write_array_to_file('phi_d_adj{}.json'.format(job),phi_d,'a')
# from IPython import embed; embed()
plotter.update_plot(phi_ic, phi_d, y, x_N, j)
print "* * * J = {}".format(j)
tic()
return func_value
def similarity_test(plot, show, save):
model = sw.Model()
model.plot = plot
model.show_plot = show
model.save_plot = save
# mesh
model.dX_ = 5.0e-3
model.L_ = 1.0
# current properties
model.Fr_ = 1.19
model.beta_ = 0.0
# time stepping
model.timestep = 5e-4 # model.dX_/500.0
model.adapt_timestep = False
model.adapt_initial_timestep = False
model.cfl = Constant(0.5)
# define stabilisation parameters (0.1,0.1,0.1,0.1) found to work well for t=10.0
model.q_b = Constant(0.0)
model.h_b = Constant(0.0)
model.phi_b = Constant(0.0)
model.phi_d_b = Constant(0.0)
# discretisation
model.q_degree = 1
model.h_degree = 1
model.phi_degree = 1
model.phi_d_degree = 1
model.q_disc = "DG"
model.h_disc = "DG"
model.phi_disc = "DG"
model.phi_d_disc = "DG"
model.disc = [model.q_disc, model.h_disc, model.phi_disc, model.phi_d_disc]
w_ic_e = [
"(2./3.)*K*pow(t,-1./3.)*x[0]*(4./9.)*pow(K,2.0)*pow(t,-2./3.)*(1./pow(Fr,2.0) - (1./4.) + (1./4.)*pow(x[0],2.0))",
"(4./9.)*pow(K,2.0)*pow(t,-2./3.)*(1./pow(Fr,2.0) - (1./4.) + (1./4.)*pow(x[0],2.0))",
"(4./9.)*pow(K,2.0)*pow(t,-2./3.)*(1./pow(Fr,2.0) - (1./4.) + (1./4.)*pow(x[0],2.0))",
"0.0",
"K*pow(t, (2./3.))",
"(2./3.)*K*pow(t,-1./3.)",
]
def getError(model):
Fq = FunctionSpace(model.mesh, model.q_disc, model.q_degree + 2)
Fh = FunctionSpace(model.mesh, model.h_disc, model.h_degree + 2)
Fphi = FunctionSpace(model.mesh, model.phi_disc, model.phi_degree + 2)
Fphi_d = FunctionSpace(model.mesh, model.phi_d_disc, model.phi_d_degree + 2)
K = ((27.0 * model.Fr_ ** 2.0) / (12.0 - 2.0 * model.Fr_ ** 2.0)) ** (1.0 / 3.0)
S_q = project(Expression(w_ic_e[0], K=K, Fr=model.Fr_, t=model.t, degree=5), Fq)
S_h = project(Expression(w_ic_e[1], K=K, Fr=model.Fr_, t=model.t, degree=5), Fh)
S_phi = project(Expression(w_ic_e[2], K=K, Fr=model.Fr_, t=model.t, degree=5), Fphi)
q, h, phi, phi_d, x_N, u_N = model.w[0].split()
E_q = errornorm(q, S_q, norm_type="L2", degree_rise=2)
E_h = errornorm(h, S_h, norm_type="L2", degree_rise=2)
E_phi = errornorm(phi, S_phi, norm_type="L2", degree_rise=2)
E_x_N = abs(x_N - K * model.t ** (2.0 / 3.0))
E_u_N = abs(u_N - (2.0 / 3.0) * K * model.t ** (-1.0 / 3.0))
return E_q, E_h, E_phi, 0.0, E_x_N, E_u_N
# long test
T = 1.5
dt = [1e-1, 1e-1 / 2, 1e-1 / 4, 1e-1 / 8, 1e-1 / 16, 1e-1 / 32, 1e-1 / 64, 1e-1 / 128, 1e-1 / 256, 1e-1 / 512]
dX = [1.0 / 4, 1.0 / 8, 1.0 / 16, 1.0 / 32, 1.0 / 64]
dt = [1e-1 / 32]
dX = [1.0 / 16, 1.0 / 32, 1.0 / 64]
# quick settings
T = 0.52
dt = [1e-1 / 512]
dX = [1.0 / 4, 1.0 / 8, 1.0 / 16]
E = []
for dt_ in dt:
E.append([])
for dX_ in dX:
print dX_, dt_
model.dX_ = dX_
model.timestep = dt_
model.t = 0.5
model.initialise_function_spaces()
w_ic_E = Expression(
(w_ic_e[0], w_ic_e[1], w_ic_e[2], w_ic_e[3], w_ic_e[4], w_ic_e[5]),
K=((27.0 * model.Fr_ ** 2.0) / (12.0 - 2.0 * model.Fr_ ** 2.0)) ** (1.0 / 3.0),
Fr=model.Fr_,
t=model.t,
element=model.W.ufl_element(),
degree=5,
)
w_ic = project(w_ic_E, model.W)
model.setup(w_ic=w_ic, similarity=True)
model.error_callback = getError
E[-1].append(model.solve(T))
sw_io.write_array_to_file("similarity_convergence.json", E, "w")
E = E[0]
print (
"R = 0.00 0.00 0.00 0.00 0.00 E = %.2e %.2e %.2e %.2e %.2e" % (E[0][0], E[0][1], E[0][2], E[0][4], E[0][5])
)
for i in range(1, len(E)):
rh = np.log(E[i][0] / E[i - 1][0]) / np.log(dX[i] / dX[i - 1])
rphi = np.log(E[i][1] / E[i - 1][1]) / np.log(dX[i] / dX[i - 1])
rq = np.log(E[i][2] / E[i - 1][2]) / np.log(dX[i] / dX[i - 1])
rx = np.log(E[i][4] / E[i - 1][4]) / np.log(dX[i] / dX[i - 1])
ru = np.log(E[i][5] / E[i - 1][5]) / np.log(dX[i] / dX[i - 1])
print (
"R = %-5.2f %-5.2f %-5.2f %-5.2f %-5.2f E = %.2e %.2e %.2e %.2e %.2e"
% (rh, rphi, rq, rx, ru, E[i][0], E[i][1], E[i][2], E[i][4], E[i][5])
)
T = 75.0
if (options.T): T = options.T
model.solve(T)
elif job == 1:
adjoint_setup(model)
model.initialise_function_spaces()
phi_ic = project(Expression('1.0 - 0.1*cos(pi*x[0])'), model.phi_FS)
model.setup(phi_ic = phi_ic)
y, q, h, phi, phi_d, x_N, u_N = sw_io.map_to_arrays(model.w[0], model.y, model.mesh)
sw_io.write_array_to_file('phi_ic.json', phi, 'w')
model.solve(T = options.T)
y, q, h, phi, phi_d, x_N, u_N = sw_io.map_to_arrays(model.w[0], model.y, model.mesh)
sw_io.write_array_to_file('deposit_data.json', phi_d, 'w')
sw_io.write_array_to_file('runout_data.json', [x_N], 'w')
elif job == 4:
adjoint_setup(model)
model.initialise_function_spaces()
# phi_ic = project(Expression('1.0 - (0.8*cos(pow(x[0] +0.1,4.0)*pi))'), model.phi_FS)
phi_ic = project(Expression('1.0'), model.phi_FS)
