From 25e3aa7287de2400ce8ebbc8160153c70e8757a1 Mon Sep 17 00:00:00 2001
From: David Seus <david.seus@ians.uni-stuttgart.de>
Date: Thu, 19 Sep 2019 14:47:17 +0200
Subject: [PATCH] test different mesh study usecases
---
LDDsimulation/LDDsimulation.py | 57 +-
.../R-one-patch-mesh-study-alternative.py | 491 ++++++++++++++++++
.../mesh_study/R-one-patch-mesh-study.py | 491 ++++++++++++++++++
.../R-one-patch-mesh-study-fixed-timestep.py | 491 ++++++++++++++++++
...h-mesh-study-fixed-timestep-nonwetting0.py | 5 +-
...atch-mesh-study-fixed-timestep-wetting0.py | 2 +-
.../TP-one-patch-mesh-study-fixed-timestep.py | 28 +-
7 files changed, 1544 insertions(+), 21 deletions(-)
create mode 100755 TP-one-patch/mesh_study/R-one-patch-mesh-study-alternative.py
create mode 100755 TP-one-patch/mesh_study/R-one-patch-mesh-study.py
create mode 100755 TP-one-patch/mesh_study_for_fixed_timestep/R-one-patch-mesh-study-fixed-timestep.py
diff --git a/LDDsimulation/LDDsimulation.py b/LDDsimulation/LDDsimulation.py
index 6da7a40..6208b6c 100644
--- a/LDDsimulation/LDDsimulation.py
+++ b/LDDsimulation/LDDsimulation.py
@@ -56,7 +56,7 @@ class LDDsimulation(object):
# df.parameters["refinement_algorithm"] = "plaza_with_parent_facets"
df.parameters["form_compiler"]["quadrature_degree"] = 12
# interpolation degree, for source terms, intitial and boundary conditions.
- self.interpolation_degree = 8
+ self.interpolation_degree = 4
# # To be able to run DG in parallel
# df.parameters["ghost_mode"] = "shared_facet"
# df.parameters["ghost_mode"] = "none"
@@ -411,6 +411,12 @@ class LDDsimulation(object):
# df.info(colored("start post processing calculations ...\n", "yellow"))
# self.post_processing()
# df.info(colored("finished post processing calculations \nAll right. I'm Done.", "green"))
+ for subdomain_index, subdomain_output in self.output.items():
+ print(f"Errornorms on subdomain{subdomain_index}")
+ for phase, different_errornorms in subdomain_output['errornorm'].items():
+ print(f"phase: {phase}")
+ for errortype, error in different_errornorms.items():
+ print(f"{errortype}: {error}\n")
return self.output
@@ -710,14 +716,34 @@ class LDDsimulation(object):
# if we have an exact solution, write out several errors and
# errornorms to be used later in paraview or latex plots.
if subdomain.pressure_exact is not None:
+ pressure_exact = dict()
for phase in subdomain.has_phases:
pa_exact = subdomain.pressure_exact[phase]
pa_exact.t = self.t
- error_calculated = df.errornorm(pa_exact, subdomain.pressure[phase], 'L2', degree_rise=6)
+ error_calculated = df.errornorm(pa_exact, subdomain.pressure[phase], 'L2', degree_rise=2)
+ pressure_exact.update(
+ {phase: df.interpolate(pa_exact, subdomain.function_space["pressure"][phase])}
+ )
+ absolute_difference = df.Function(subdomain.function_space["pressure"][phase])
+ pressure_difference = pressure_exact[phase].vector()[:] - subdomain.pressure[phase].vector()[:]
+ abs_diff_tmp = np.fabs(pressure_difference)
+ absolute_difference.vector()[:] = abs_diff_tmp
+ dx = subdomain.dx
+ error_calculated_L1 = df.assemble(absolute_difference*dx)
+ error_calculated_L2 = np.sqrt(df.assemble(absolute_difference**2*dx))
+ error_calculated_L2_2 = df.norm(absolute_difference, norm_type='L2', mesh=subdomain.mesh)
+ print(f"Errornorm dolfin: {error_calculated}")
+ print(f"Errornorm manually calculated L1: {error_calculated_L1}")
+ print(f"Errornorm manually calculated L2: {error_calculated_L2}")
+ print(f"Errornorm manually calculated L2 with df.norm: {error_calculated_L2_2}")
self.output[subdom_ind]['errornorm'][phase]['L1'] += self.timestep_size*error_calculated
self.output[subdom_ind]['errornorm'][phase]['L2'] += self.timestep_size*error_calculated**2
+ print(f"Linf error on subdomain {subdom_ind} and phase {phase} before checking: {self.output[subdom_ind]['errornorm'][phase]['Linf']}")
if error_calculated > self.output[subdom_ind]['errornorm'][phase]['Linf']:
- self.output[subdom_ind]['errornorm'][phase]['Linf'] = error_calculated
+ self.output[subdom_ind]['errornorm'][phase].update(
+ {'Linf': error_calculated}
+ )
+ print(f"Linf error on subdomain {subdom_ind} and phase {phase} after checking: {self.output[subdom_ind]['errornorm'][phase]['Linf']}")
# if we are at a timestep at which to write shit out,
# calculate the relative errornorm
@@ -868,20 +894,33 @@ class LDDsimulation(object):
"""
evaluate the exact solution of the simulation (in case there is one) at
all timesteps and write it to the solution file.
+ In addition write calculate and write out the saturation as well as the
+ source terms in order to montior the examples
"""
# print(f" solution will be printed at times t = {self.timesteps_to_plot}\n")
for subdom_ind, subdomain in self.subdomain.items():
file = self.solution_file[subdom_ind]
for timestep in self.timesteps_to_plot:
exact_pressure = dict()
+ S = self.saturation[subdom_ind]
+ saturation_w = df.Function(subdomain.function_space["pressure"]['wetting'])
+ saturation_nw = df.Function(subdomain.function_space["pressure"]['wetting'])
+ source = dict()
for phase in subdomain.has_phases:
+ f_expr = subdomain.source[phase]
pa_exact = subdomain.pressure_exact[phase]
pa_exact.t = timestep
+ f_expr.t = timestep
exact_pressure.update(
- {phase: df.interpolate(pa_exact, subdomain.function_space["pressure"][phase])}
+ {phase: df.project(pa_exact, subdomain.function_space["pressure"][phase])}
)
+ source.update(
+ {phase: df.project(f_expr, subdomain.function_space["pressure"][phase])}
+ )
exact_pressure[phase].rename("exact_pressure_"+"{}".format(phase), "exact_pressure_"+"{}".format(phase))
file.write(exact_pressure[phase], timestep)
+ source[phase].rename("source_"+"{}".format(phase), "source_"+"{}".format(phase))
+ file.write(source[phase], timestep)
exact_capillary_pressure = df.Function(subdomain.function_space["pressure"]['wetting'])
if subdomain.isRichards:
@@ -891,6 +930,15 @@ class LDDsimulation(object):
exact_capillary_pressure.vector().set_local(pc_temp)
exact_capillary_pressure.rename("pc_exact", "pc_exact")
file.write(exact_capillary_pressure, timestep)
+ saturation_w = df.project(S(exact_capillary_pressure), subdomain.function_space["pressure"]["wetting"])
+ # saturation_w.assign(Sat_w)
+ saturation_w.rename("Sw", "Sw")
+ file.write(saturation_w, timestep)
+ # S_nw = 1-S(exact_capillary_pressure).vector().get_local()
+ saturation_nw = df.project(1-S(exact_capillary_pressure), subdomain.function_space["pressure"]["wetting"])
+ # saturation_nw.assign(S_nw)
+ saturation_nw.rename("Snw", "Snw")
+ file.write(saturation_nw, timestep)
def write_subsequent_errors_to_csv(self,#
@@ -1390,6 +1438,7 @@ class LDDsimulation(object):
# in case time == self.starttime, the expression has already been
# assembled by self._init_DirichletBC_dictionary.
if np.fabs(time - self.starttime) < self.tol:
+ print("warning: update_DirichletBC_dictionary tried to update initial time")
pass
else:
V = subdomain.function_space["pressure"]
diff --git a/TP-one-patch/mesh_study/R-one-patch-mesh-study-alternative.py b/TP-one-patch/mesh_study/R-one-patch-mesh-study-alternative.py
new file mode 100755
index 0000000..8255953
--- /dev/null
+++ b/TP-one-patch/mesh_study/R-one-patch-mesh-study-alternative.py
@@ -0,0 +1,491 @@
+#!/usr/bin/python3
+import dolfin as df
+import mshr
+import numpy as np
+import sympy as sym
+import typing as tp
+import domainPatch as dp
+import LDDsimulation as ldd
+import functools as ft
+import helpers as hlp
+import datetime
+import os
+import pandas as pd
+
+date = datetime.datetime.now()
+datestr = date.strftime("%Y-%m-%d")
+#import ufl as ufl
+
+# init sympy session
+sym.init_printing()
+
+use_case = "R-one-patch-mesh-study"
+# solver_tol = 5E-9
+max_iter_num = 1000
+FEM_Lagrange_degree = 1
+mesh_study = True
+# resolutions = {128: 1e-7} #[1,2,3,4,5,10,20,40,75,100]
+resolutions = {
+ # 1: 1e-7,
+ # 2: 1e-7,
+ # 4: 1e-7,
+ # 8: 1e-7,
+ # 16: 1e-7,
+ 32: 1e-7,
+ # 64: 1e-7,
+ # 128: 1e-7,
+ # 256: 1e-7,
+ # 512: 1e-7,
+ }
+
+############ GRID #######################
+# mesh_resolution = 20
+timestep_size = 0.001
+number_of_timesteps = 10
+plot_timestep_every = 1
+# decide how many timesteps you want analysed. Analysed means, that we write out
+# subsequent errors of the L-iteration within the timestep.
+number_of_timesteps_to_analyse = 5
+starttimes = [0.5]
+# starttimes = [0.0, 0.05]
+
+# starttimes = {
+# 1: 0.0
+# 2: 0.05
+# 4: 0.1
+# 8: 0.2
+# 16: 0.4
+# 32: 0.7
+# 64: 1.0
+# 128: 1.3
+# }
+
+Lw = 0.5 #/timestep_size
+Lnw=Lw
+
+lambda_w = 0
+lambda_nw = 0
+
+include_gravity = False
+debugflag = False
+analyse_condition = True
+
+if mesh_study:
+ output_string = "./output/{}-{}_timesteps{}_P{}".format(datestr, use_case, number_of_timesteps, FEM_Lagrange_degree)
+else:
+ for tol in resolutions.values():
+ solver_tol = tol
+ output_string = "./output/{}-{}_timesteps{}_P{}_solver_tol{}".format(datestr, use_case, number_of_timesteps, FEM_Lagrange_degree, solver_tol)
+
+# toggle what should be written to files
+if mesh_study:
+ write_to_file = {
+ 'space_errornorms': True,
+ 'meshes_and_markers': True,
+ 'L_iterations_per_timestep': True,
+ 'solutions': True,
+ 'absolute_differences': True,
+ 'condition_numbers': analyse_condition,
+ 'subsequent_errors': True
+ }
+else:
+ write_to_file = {
+ 'space_errornorms': True,
+ 'meshes_and_markers': True,
+ 'L_iterations_per_timestep': False,
+ 'solutions': True,
+ 'absolute_differences': True,
+ 'condition_numbers': analyse_condition,
+ 'subsequent_errors': True
+ }
+
+##### Domain and Interface ####
+# global simulation domain domain
+sub_domain0_vertices = [df.Point(-1.0, -1.0), #
+ df.Point(1.0, -1.0), #
+ df.Point(1.0, 1.0), #
+ df.Point(-1.0, 1.0)]
+
+subdomain0_outer_boundary_verts = {
+ 0: [sub_domain0_vertices[0],
+ sub_domain0_vertices[1],
+ sub_domain0_vertices[2],
+ sub_domain0_vertices[3],
+ sub_domain0_vertices[0]]
+}
+
+# list of subdomains given by the boundary polygon vertices.
+# Subdomains are given as a list of dolfin points forming
+# a closed polygon, such that mshr.Polygon(subdomain_def_points[i]) can be used
+# to create the subdomain. subdomain_def_points[0] contains the
+# vertices of the global simulation domain and subdomain_def_points[i] contains the
+# vertices of the subdomain i.
+subdomain_def_points = [sub_domain0_vertices]
+# in the below list, index 0 corresponds to the 12 interface which has index 1
+interface_def_points = None
+
+# if a subdomain has no outer boundary write None instead, i.e.
+# i: None
+# if i is the index of the inner subdomain.
+outer_boundary_def_points = {
+ # subdomain number
+ 0 : subdomain0_outer_boundary_verts
+}
+
+# adjacent_subdomains[i] contains the indices of the subdomains sharing the
+# interface i (i.e. given by interface_def_points[i]).
+adjacent_subdomains = None
+isRichards = {
+ 0: True, #
+ }
+
+viscosity = {#
+# subdom_num : viscosity
+ 0 : {'wetting' :1,
+ 'nonwetting': 1}, #
+}
+
+porosity = {#
+# subdom_num : porosity
+ 0: 1,#
+}
+
+# Dict of the form: { subdom_num : density }
+densities = {
+ 0: {'wetting': 1, #997,
+ 'nonwetting': 1}, #1225}
+}
+
+gravity_acceleration = 9.81
+
+L = {#
+# subdom_num : subdomain L for L-scheme
+ 0: {'wetting' :Lw,
+ 'nonwetting': Lnw},#
+}
+
+lambda_param = {#
+# subdom_num : lambda parameter for the L-scheme
+ 0: {'wetting' :lambda_w,
+ 'nonwetting': lambda_nw},#
+}
+
+## relative permeabilty functions on subdomain 1
+def rel_perm1w(s):
+ # relative permeabilty wetting on subdomain1
+ return s**2
+
+def rel_perm1nw(s):
+ # relative permeabilty nonwetting on subdomain1
+ return (1-s)**2
+
+_rel_perm1w = ft.partial(rel_perm1w)
+_rel_perm1nw = ft.partial(rel_perm1nw)
+
+subdomain1_rel_perm = {
+ 'wetting': _rel_perm1w,#
+ 'nonwetting': _rel_perm1nw
+}
+
+## dictionary of relative permeabilties on all domains.
+relative_permeability = {#
+ 0: subdomain1_rel_perm,
+}
+
+# definition of the derivatives of the relative permeabilities
+# relative permeabilty functions on subdomain 1
+def rel_perm1w_prime(s):
+ # relative permeabilty on subdomain1
+ return 2*s
+
+def rel_perm1nw_prime(s):
+ # relative permeabilty on subdomain1
+ return -2*(1-s)
+
+_rel_perm1w_prime = ft.partial(rel_perm1w_prime)
+_rel_perm1nw_prime = ft.partial(rel_perm1nw_prime)
+
+subdomain1_rel_perm_prime = {
+ 'wetting': _rel_perm1w_prime,
+ 'nonwetting': _rel_perm1nw_prime
+}
+
+# dictionary of relative permeabilties on all domains.
+ka_prime = {
+ 0: subdomain1_rel_perm_prime,
+}
+
+
+
+def saturation(pc, index):
+ # inverse capillary pressure-saturation-relationship
+ return df.conditional(pc > 0, 1/((1 + pc)**(1/(index + 1))), 1)
+
+def saturation_sym(pc, index):
+ # inverse capillary pressure-saturation-relationship
+ return 1/((1 + pc)**(1/(index + 1)))
+
+
+# derivative of S-pc relationship with respect to pc. This is needed for the
+# construction of a analytic solution.
+def saturation_sym_prime(pc, index):
+ # inverse capillary pressure-saturation-relationship
+ return -1/((index+1)*(1 + pc)**((index+2)/(index+1)))
+
+
+# def saturation(pc, index):
+# # inverse capillary pressure-saturation-relationship
+# return df.conditional(pc > 0, -index*pc, 1)
+#
+#
+# def saturation_sym(pc, index):
+# # inverse capillary pressure-saturation-relationship
+# return -index*pc
+#
+#
+# # derivative of S-pc relationship with respect to pc. This is needed for the
+# # construction of a analytic solution.
+# def saturation_sym_prime(pc, index):
+# # inverse capillary pressure-saturation-relationship
+# return -index
+
+
+# note that the conditional definition of S-pc in the nonsymbolic part will be
+# incorporated in the construction of the exact solution below.
+S_pc_sym = {
+ 0: ft.partial(saturation_sym, index=1),
+}
+
+S_pc_sym_prime = {
+ 0: ft.partial(saturation_sym_prime, index=1),
+}
+
+sat_pressure_relationship = {
+ 0: ft.partial(saturation, index=1),
+}
+
+
+#############################################
+# Manufacture source expressions with sympy #
+#############################################
+x, y = sym.symbols('x[0], x[1]') # needed by UFL
+t = sym.symbols('t', positive=True)
+
+epsilon_x_inner = 0.7
+epsilon_x_outer = 0.99
+epsilon_y_inner = epsilon_x_inner
+epsilon_y_outer = epsilon_x_outer
+
+def mollifier(x, epsilon):
+ """ one d mollifier """
+ out_expr = sym.exp(-1/(1-(x/epsilon)**2) + 1)
+ return out_expr
+
+mollifier_handle = ft.partial(mollifier, epsilon=epsilon_x_inner)
+
+pw_sym_x = sym.Piecewise(
+ (mollifier_handle(x), x**2 < epsilon_x_outer**2),
+ (0, True)
+)
+pw_sym_y = sym.Piecewise(
+ (mollifier_handle(y), y**2 < epsilon_y_outer**2),
+ (0, True)
+)
+
+def mollifier2d(x, y, epsilon):
+ """ one d mollifier """
+ out_expr = sym.exp(-1/(1-(x**2 + y**2)/epsilon**2) + 1)
+ return out_expr
+
+mollifier2d_handle = ft.partial(mollifier2d, epsilon=epsilon_x_outer)
+
+pw_sym2d_x = sym.Piecewise(
+ (mollifier2d_handle(x, y), x**2 + y**2 < epsilon_x_outer**2),
+ (0, True)
+)
+
+zero_on_epsilon_shrinking_of_subdomain = sym.Piecewise(
+ (mollifier_handle(sym.sqrt(x**2 + y**2)+2*epsilon_x_inner), ((-2*epsilon_x_inner<sym.sqrt(x**2 + y**2)) & (sym.sqrt(x**2 + y**2)<-epsilon_x_inner))),
+ (0, ((-epsilon_x_inner<=sym.sqrt(x**2 + y**2)) & (sym.sqrt(x**2 + y**2)<=epsilon_x_inner))),
+ (mollifier_handle(sym.sqrt(x**2 + y**2)-2*epsilon_x_inner), ((epsilon_x_inner<sym.sqrt(x**2 + y**2)) & (sym.sqrt(x**2 + y**2)<2*epsilon_x_inner))),
+ (1, True),
+)
+
+zero_on_epsilon_shrinking_of_subdomain_x = sym.Piecewise(
+ (mollifier_handle(x+2*epsilon_x_inner), ((-2*epsilon_x_inner<x) & (x<-epsilon_x_inner))),
+ (0, ((-epsilon_x_inner<=x) & (x<=epsilon_x_inner))),
+ (mollifier_handle(x-2*epsilon_x_inner), ((epsilon_x_inner<x) & (x<2*epsilon_x_inner))),
+ (1, True),
+)
+
+zero_on_epsilon_shrinking_of_subdomain_y = sym.Piecewise(
+ (1, y<=-2*epsilon_x_inner),
+ (mollifier_handle(y+2*epsilon_x_inner), ((-2*epsilon_x_inner<y) & (y<-epsilon_x_inner))),
+ (0, ((-epsilon_x_inner<=y) & (y<=epsilon_x_inner))),
+ (mollifier_handle(y-2*epsilon_x_inner), ((epsilon_x_inner<y) & (y<2*epsilon_x_inner))),
+ (1, True),
+)
+
+zero_on_shrinking = zero_on_epsilon_shrinking_of_subdomain #zero_on_epsilon_shrinking_of_subdomain_x + zero_on_epsilon_shrinking_of_subdomain_y
+gaussian = pw_sym2d_x# pw_sym_y*pw_sym_x
+cutoff = gaussian/(gaussian + zero_on_shrinking)
+
+# # construction of differentiable characteristic function.
+# def smooth_characteristic_func_on_epsilon_shrinking_of_subdomain0(x, y, epsilon_x_inner, epsilon_y_inner, epsilon_x_outer, epsilon_y_outer):
+# dist_to_complement_x = ft.partial(mollifier, epsilon=epsilon_x_inner)
+# dist_to_complement_y = ft.partial(mollifier, epsilon=epsilon_y_inner)
+# dist_to_complement = dist_to_complement_y(y)*dist_to_complement_x(x)
+# dist_to_eps_shrinking_x = ft.partial(zero_outside_epsilon_thickening_of_subdomain, epsilon=epsilon_x_outer)
+# dist_to_eps_shrinking_y = ft.partial(zero_outside_epsilon_thickening_of_subdomain, epsilon=epsilon_y_outer)
+# dist_to_eps_shrinking = dist_to_eps_shrinking_y(y)*dist_to_eps_shrinking_x(x)
+# return dist_to_complement/(dist_to_eps_shrinking + dist_to_complement)
+#
+
+# def dist_to_epsilon_thickening_of_subdomain0_complement(x, y, epsilon):
+# """ calculates the (euklidian distance)^2 of a point x,y to the epsilon
+# thickening of the complement of the domain.
+# """
+# is_inside = ((1-sym.Abs(x) > epsilon) & (1-sym.Abs(y) > epsilon))
+# sym.Piecewise((0, is_inside))
+
+p_e_sym = {
+ 0: {'wetting': (-7 -1*t*(1 + x + y)), #*cutoff,
+ 'nonwetting': (-1 -1*t*(1.1+y + x))}, #*cutoff},
+}
+
+pc_e_sym = dict()
+for subdomain, isR in isRichards.items():
+ if isR:
+ pc_e_sym.update({subdomain: -p_e_sym[subdomain]['wetting']})
+ else:
+ pc_e_sym.update({subdomain: p_e_sym[subdomain]['nonwetting']
+ - p_e_sym[subdomain]['wetting']})
+
+
+symbols = {"x": x,
+ "y": y,
+ "t": t}
+# turn above symbolic code into exact solution for dolphin and
+# construct the rhs that matches the above exact solution.
+exact_solution_example = hlp.generate_exact_solution_expressions(
+ symbols=symbols,
+ isRichards=isRichards,
+ symbolic_pressure=p_e_sym,
+ symbolic_capillary_pressure=pc_e_sym,
+ saturation_pressure_relationship=S_pc_sym,
+ saturation_pressure_relationship_prime=S_pc_sym_prime,
+ viscosity=viscosity,
+ porosity=porosity,
+ relative_permeability=relative_permeability,
+ relative_permeability_prime=ka_prime,
+ densities=densities,
+ gravity_acceleration=gravity_acceleration,
+ include_gravity=include_gravity,
+ )
+source_expression = exact_solution_example['source']
+exact_solution = exact_solution_example['exact_solution']
+initial_condition = exact_solution_example['initial_condition']
+
+# Dictionary of dirichlet boundary conditions.
+dirichletBC = dict()
+# similarly to the outer boundary dictionary, if a patch has no outer boundary
+# None should be written instead of an expression.
+# This is a bit of a brainfuck:
+# dirichletBC[ind] gives a dictionary of the outer boundaries of subdomain ind.
+# Since a domain patch can have several disjoint outer boundary parts, the
+# expressions need to get an enumaration index which starts at 0.
+# So dirichletBC[ind][j] is the dictionary of outer dirichlet conditions of
+# subdomain ind and boundary part j.
+# Finally, dirichletBC[ind][j]['wetting'] and dirichletBC[ind][j]['nonwetting']
+# return the actual expression needed for the dirichlet condition for both
+# phases if present.
+
+# subdomain index: {outer boudary part index: {phase: expression}}
+for subdomain in isRichards.keys():
+ # if subdomain has no outer boundary, outer_boundary_def_points[subdomain] is None
+ if outer_boundary_def_points[subdomain] is None:
+ dirichletBC.update({subdomain: None})
+ else:
+ dirichletBC.update({subdomain: dict()})
+ # set the dirichlet conditions to be the same code as exact solution on
+ # the subdomain.
+ for outer_boundary_ind in outer_boundary_def_points[subdomain].keys():
+ dirichletBC[subdomain].update(
+ {outer_boundary_ind: exact_solution[subdomain]}
+ )
+
+
+# def saturation(pressure, subdomain_index):
+# # inverse capillary pressure-saturation-relationship
+# return df.conditional(pressure < 0, 1/((1 - pressure)**(1/(subdomain_index + 1))), 1)
+#
+# sa
+for starttime in starttimes:
+ for mesh_resolution, solver_tol in resolutions.items():
+ # initialise LDD simulation class
+ simulation = ldd.LDDsimulation(
+ tol=1E-14,
+ LDDsolver_tol=solver_tol,
+ debug=debugflag,
+ max_iter_num=max_iter_num,
+ FEM_Lagrange_degree=FEM_Lagrange_degree,
+ mesh_study=mesh_study
+ )
+
+ simulation.set_parameters(use_case=use_case,
+ output_dir=output_string,
+ subdomain_def_points=subdomain_def_points,
+ isRichards=isRichards,
+ interface_def_points=interface_def_points,
+ outer_boundary_def_points=outer_boundary_def_points,
+ adjacent_subdomains=adjacent_subdomains,
+ mesh_resolution=mesh_resolution,
+ viscosity=viscosity,
+ porosity=porosity,
+ L=L,
+ lambda_param=lambda_param,
+ relative_permeability=relative_permeability,
+ saturation=sat_pressure_relationship,
+ starttime=starttime,
+ number_of_timesteps=number_of_timesteps,
+ number_of_timesteps_to_analyse=number_of_timesteps_to_analyse,
+ plot_timestep_every=plot_timestep_every,
+ timestep_size=timestep_size,
+ sources=source_expression,
+ initial_conditions=initial_condition,
+ dirichletBC_expression_strings=dirichletBC,
+ exact_solution=exact_solution,
+ densities=densities,
+ include_gravity=include_gravity,
+ write2file=write_to_file,
+ )
+
+ simulation.initialise()
+ output_dir = simulation.output_dir
+ # simulation.write_exact_solution_to_xdmf()
+ output = simulation.run(analyse_condition=analyse_condition)
+ for subdomain_index, subdomain_output in output.items():
+ mesh_h = subdomain_output['mesh_size']
+ for phase, different_errornorms in subdomain_output['errornorm'].items():
+ filename = output_dir + "subdomain{}-space-time-errornorm-{}-phase.csv".format(subdomain_index, phase)
+ # for errortype, errornorm in different_errornorms.items():
+
+ # eocfile = open("eoc_filename", "a")
+ # eocfile.write( str(mesh_h) + " " + str(errornorm) + "\n" )
+ # eocfile.close()
+ # if subdomain.isRichards:mesh_h
+ data_dict = {
+ 'mesh_parameter': mesh_resolution,
+ 'mesh_h': mesh_h,
+ }
+ for error_type, errornorms in different_errornorms.items():
+ data_dict.update(
+ {error_type: errornorms}
+ )
+ errors = pd.DataFrame(data_dict, index=[mesh_resolution])
+ # check if file exists
+ if os.path.isfile(filename) == True:
+ with open(filename, 'a') as f:
+ errors.to_csv(f, header=False, sep='\t', encoding='utf-8', index=False)
+ else:
+ errors.to_csv(filename, sep='\t', encoding='utf-8', index=False)
diff --git a/TP-one-patch/mesh_study/R-one-patch-mesh-study.py b/TP-one-patch/mesh_study/R-one-patch-mesh-study.py
new file mode 100755
index 0000000..fac5fc9
--- /dev/null
+++ b/TP-one-patch/mesh_study/R-one-patch-mesh-study.py
@@ -0,0 +1,491 @@
+#!/usr/bin/python3
+import dolfin as df
+import mshr
+import numpy as np
+import sympy as sym
+import typing as tp
+import domainPatch as dp
+import LDDsimulation as ldd
+import functools as ft
+import helpers as hlp
+import datetime
+import os
+import pandas as pd
+
+date = datetime.datetime.now()
+datestr = date.strftime("%Y-%m-%d")
+#import ufl as ufl
+
+# init sympy session
+sym.init_printing()
+
+use_case = "R-one-patch-mesh-study"
+# solver_tol = 5E-9
+max_iter_num = 1000
+FEM_Lagrange_degree = 1
+mesh_study = True
+# resolutions = {128: 1e-7} #[1,2,3,4,5,10,20,40,75,100]
+resolutions = {
+ # 1: 1e-7,
+ # 2: 1e-7,
+ # 4: 1e-7,
+ # 8: 1e-7,
+ # 16: 1e-7,
+ 32: 1e-7,
+ # 64: 1e-7,
+ # 128: 1e-7,
+ # 256: 1e-7,
+ # 512: 1e-7,
+ }
+
+############ GRID #######################
+# mesh_resolution = 20
+timestep_size = 0.00001
+number_of_timesteps = 10
+plot_timestep_every = 1
+# decide how many timesteps you want analysed. Analysed means, that we write out
+# subsequent errors of the L-iteration within the timestep.
+number_of_timesteps_to_analyse = 5
+starttimes = [0.5]
+# starttimes = [0.0, 0.05]
+
+# starttimes = {
+# 1: 0.0
+# 2: 0.05
+# 4: 0.1
+# 8: 0.2
+# 16: 0.4
+# 32: 0.7
+# 64: 1.0
+# 128: 1.3
+# }
+
+Lw = 0.025 #/timestep_size
+Lnw=Lw
+
+lambda_w = 0
+lambda_nw = 0
+
+include_gravity = False
+debugflag = False
+analyse_condition = True
+
+if mesh_study:
+ output_string = "./output/{}-{}_timesteps{}_P{}".format(datestr, use_case, number_of_timesteps, FEM_Lagrange_degree)
+else:
+ for tol in resolutions.values():
+ solver_tol = tol
+ output_string = "./output/{}-{}_timesteps{}_P{}_solver_tol{}".format(datestr, use_case, number_of_timesteps, FEM_Lagrange_degree, solver_tol)
+
+# toggle what should be written to files
+if mesh_study:
+ write_to_file = {
+ 'space_errornorms': True,
+ 'meshes_and_markers': True,
+ 'L_iterations_per_timestep': True,
+ 'solutions': True,
+ 'absolute_differences': True,
+ 'condition_numbers': analyse_condition,
+ 'subsequent_errors': True
+ }
+else:
+ write_to_file = {
+ 'space_errornorms': True,
+ 'meshes_and_markers': True,
+ 'L_iterations_per_timestep': False,
+ 'solutions': True,
+ 'absolute_differences': True,
+ 'condition_numbers': analyse_condition,
+ 'subsequent_errors': True
+ }
+
+##### Domain and Interface ####
+# global simulation domain domain
+sub_domain0_vertices = [df.Point(-1.0, -1.0), #
+ df.Point(1.0, -1.0), #
+ df.Point(1.0, 1.0), #
+ df.Point(-1.0, 1.0)]
+
+subdomain0_outer_boundary_verts = {
+ 0: [sub_domain0_vertices[0],
+ sub_domain0_vertices[1],
+ sub_domain0_vertices[2],
+ sub_domain0_vertices[3],
+ sub_domain0_vertices[0]]
+}
+
+# list of subdomains given by the boundary polygon vertices.
+# Subdomains are given as a list of dolfin points forming
+# a closed polygon, such that mshr.Polygon(subdomain_def_points[i]) can be used
+# to create the subdomain. subdomain_def_points[0] contains the
+# vertices of the global simulation domain and subdomain_def_points[i] contains the
+# vertices of the subdomain i.
+subdomain_def_points = [sub_domain0_vertices]
+# in the below list, index 0 corresponds to the 12 interface which has index 1
+interface_def_points = None
+
+# if a subdomain has no outer boundary write None instead, i.e.
+# i: None
+# if i is the index of the inner subdomain.
+outer_boundary_def_points = {
+ # subdomain number
+ 0 : subdomain0_outer_boundary_verts
+}
+
+# adjacent_subdomains[i] contains the indices of the subdomains sharing the
+# interface i (i.e. given by interface_def_points[i]).
+adjacent_subdomains = None
+isRichards = {
+ 0: True, #
+ }
+
+viscosity = {#
+# subdom_num : viscosity
+ 0 : {'wetting' :1,
+ 'nonwetting': 1}, #
+}
+
+porosity = {#
+# subdom_num : porosity
+ 0: 1,#
+}
+
+# Dict of the form: { subdom_num : density }
+densities = {
+ 0: {'wetting': 1, #997,
+ 'nonwetting': 1}, #1225}
+}
+
+gravity_acceleration = 9.81
+
+L = {#
+# subdom_num : subdomain L for L-scheme
+ 0: {'wetting' :Lw,
+ 'nonwetting': Lnw},#
+}
+
+lambda_param = {#
+# subdom_num : lambda parameter for the L-scheme
+ 0: {'wetting' :lambda_w,
+ 'nonwetting': lambda_nw},#
+}
+
+## relative permeabilty functions on subdomain 1
+def rel_perm1w(s):
+ # relative permeabilty wetting on subdomain1
+ return s**2
+
+def rel_perm1nw(s):
+ # relative permeabilty nonwetting on subdomain1
+ return (1-s)**2
+
+_rel_perm1w = ft.partial(rel_perm1w)
+_rel_perm1nw = ft.partial(rel_perm1nw)
+
+subdomain1_rel_perm = {
+ 'wetting': _rel_perm1w,#
+ 'nonwetting': _rel_perm1nw
+}
+
+## dictionary of relative permeabilties on all domains.
+relative_permeability = {#
+ 0: subdomain1_rel_perm,
+}
+
+# definition of the derivatives of the relative permeabilities
+# relative permeabilty functions on subdomain 1
+def rel_perm1w_prime(s):
+ # relative permeabilty on subdomain1
+ return 2*s
+
+def rel_perm1nw_prime(s):
+ # relative permeabilty on subdomain1
+ return -2*(1-s)
+
+_rel_perm1w_prime = ft.partial(rel_perm1w_prime)
+_rel_perm1nw_prime = ft.partial(rel_perm1nw_prime)
+
+subdomain1_rel_perm_prime = {
+ 'wetting': _rel_perm1w_prime,
+ 'nonwetting': _rel_perm1nw_prime
+}
+
+# dictionary of relative permeabilties on all domains.
+ka_prime = {
+ 0: subdomain1_rel_perm_prime,
+}
+
+
+
+def saturation(pc, index):
+ # inverse capillary pressure-saturation-relationship
+ return df.conditional(pc > 0, 1/((1 + pc)**(1/(index + 1))), 1)
+
+def saturation_sym(pc, index):
+ # inverse capillary pressure-saturation-relationship
+ return 1/((1 + pc)**(1/(index + 1)))
+
+
+# derivative of S-pc relationship with respect to pc. This is needed for the
+# construction of a analytic solution.
+def saturation_sym_prime(pc, index):
+ # inverse capillary pressure-saturation-relationship
+ return -1/((index+1)*(1 + pc)**((index+2)/(index+1)))
+
+
+# def saturation(pc, index):
+# # inverse capillary pressure-saturation-relationship
+# return df.conditional(pc > 0, -index*pc, 1)
+#
+#
+# def saturation_sym(pc, index):
+# # inverse capillary pressure-saturation-relationship
+# return -index*pc
+#
+#
+# # derivative of S-pc relationship with respect to pc. This is needed for the
+# # construction of a analytic solution.
+# def saturation_sym_prime(pc, index):
+# # inverse capillary pressure-saturation-relationship
+# return -index
+
+
+# note that the conditional definition of S-pc in the nonsymbolic part will be
+# incorporated in the construction of the exact solution below.
+S_pc_sym = {
+ 0: ft.partial(saturation_sym, index=1),
+}
+
+S_pc_sym_prime = {
+ 0: ft.partial(saturation_sym_prime, index=1),
+}
+
+sat_pressure_relationship = {
+ 0: ft.partial(saturation, index=1),
+}
+
+
+#############################################
+# Manufacture source expressions with sympy #
+#############################################
+x, y = sym.symbols('x[0], x[1]') # needed by UFL
+t = sym.symbols('t', positive=True)
+
+epsilon_x_inner = 0.7
+epsilon_x_outer = 0.99
+epsilon_y_inner = epsilon_x_inner
+epsilon_y_outer = epsilon_x_outer
+
+def mollifier(x, epsilon):
+ """ one d mollifier """
+ out_expr = sym.exp(-1/(1-(x/epsilon)**2) + 1)
+ return out_expr
+
+mollifier_handle = ft.partial(mollifier, epsilon=epsilon_x_inner)
+
+pw_sym_x = sym.Piecewise(
+ (mollifier_handle(x), x**2 < epsilon_x_outer**2),
+ (0, True)
+)
+pw_sym_y = sym.Piecewise(
+ (mollifier_handle(y), y**2 < epsilon_y_outer**2),
+ (0, True)
+)
+
+def mollifier2d(x, y, epsilon):
+ """ one d mollifier """
+ out_expr = sym.exp(-1/(1-(x**2 + y**2)/epsilon**2) + 1)
+ return out_expr
+
+mollifier2d_handle = ft.partial(mollifier2d, epsilon=epsilon_x_outer)
+
+pw_sym2d_x = sym.Piecewise(
+ (mollifier2d_handle(x, y), x**2 + y**2 < epsilon_x_outer**2),
+ (0, True)
+)
+
+zero_on_epsilon_shrinking_of_subdomain = sym.Piecewise(
+ (mollifier_handle(sym.sqrt(x**2 + y**2)+2*epsilon_x_inner), ((-2*epsilon_x_inner<sym.sqrt(x**2 + y**2)) & (sym.sqrt(x**2 + y**2)<-epsilon_x_inner))),
+ (0, ((-epsilon_x_inner<=sym.sqrt(x**2 + y**2)) & (sym.sqrt(x**2 + y**2)<=epsilon_x_inner))),
+ (mollifier_handle(sym.sqrt(x**2 + y**2)-2*epsilon_x_inner), ((epsilon_x_inner<sym.sqrt(x**2 + y**2)) & (sym.sqrt(x**2 + y**2)<2*epsilon_x_inner))),
+ (1, True),
+)
+
+zero_on_epsilon_shrinking_of_subdomain_x = sym.Piecewise(
+ (mollifier_handle(x+2*epsilon_x_inner), ((-2*epsilon_x_inner<x) & (x<-epsilon_x_inner))),
+ (0, ((-epsilon_x_inner<=x) & (x<=epsilon_x_inner))),
+ (mollifier_handle(x-2*epsilon_x_inner), ((epsilon_x_inner<x) & (x<2*epsilon_x_inner))),
+ (1, True),
+)
+
+zero_on_epsilon_shrinking_of_subdomain_y = sym.Piecewise(
+ (1, y<=-2*epsilon_x_inner),
+ (mollifier_handle(y+2*epsilon_x_inner), ((-2*epsilon_x_inner<y) & (y<-epsilon_x_inner))),
+ (0, ((-epsilon_x_inner<=y) & (y<=epsilon_x_inner))),
+ (mollifier_handle(y-2*epsilon_x_inner), ((epsilon_x_inner<y) & (y<2*epsilon_x_inner))),
+ (1, True),
+)
+
+zero_on_shrinking = zero_on_epsilon_shrinking_of_subdomain #zero_on_epsilon_shrinking_of_subdomain_x + zero_on_epsilon_shrinking_of_subdomain_y
+gaussian = pw_sym2d_x# pw_sym_y*pw_sym_x
+cutoff = gaussian/(gaussian + zero_on_shrinking)
+
+# # construction of differentiable characteristic function.
+# def smooth_characteristic_func_on_epsilon_shrinking_of_subdomain0(x, y, epsilon_x_inner, epsilon_y_inner, epsilon_x_outer, epsilon_y_outer):
+# dist_to_complement_x = ft.partial(mollifier, epsilon=epsilon_x_inner)
+# dist_to_complement_y = ft.partial(mollifier, epsilon=epsilon_y_inner)
+# dist_to_complement = dist_to_complement_y(y)*dist_to_complement_x(x)
+# dist_to_eps_shrinking_x = ft.partial(zero_outside_epsilon_thickening_of_subdomain, epsilon=epsilon_x_outer)
+# dist_to_eps_shrinking_y = ft.partial(zero_outside_epsilon_thickening_of_subdomain, epsilon=epsilon_y_outer)
+# dist_to_eps_shrinking = dist_to_eps_shrinking_y(y)*dist_to_eps_shrinking_x(x)
+# return dist_to_complement/(dist_to_eps_shrinking + dist_to_complement)
+#
+
+# def dist_to_epsilon_thickening_of_subdomain0_complement(x, y, epsilon):
+# """ calculates the (euklidian distance)^2 of a point x,y to the epsilon
+# thickening of the complement of the domain.
+# """
+# is_inside = ((1-sym.Abs(x) > epsilon) & (1-sym.Abs(y) > epsilon))
+# sym.Piecewise((0, is_inside))
+
+p_e_sym = {
+ 0: {'wetting': (-7 - (1+t*t)*(1 + x*x + y*y)), #*cutoff,
+ 'nonwetting': (-1 -t*(1.1+y + x**2))}, #*cutoff},
+}
+
+pc_e_sym = dict()
+for subdomain, isR in isRichards.items():
+ if isR:
+ pc_e_sym.update({subdomain: -p_e_sym[subdomain]['wetting']})
+ else:
+ pc_e_sym.update({subdomain: p_e_sym[subdomain]['nonwetting']
+ - p_e_sym[subdomain]['wetting']})
+
+
+symbols = {"x": x,
+ "y": y,
+ "t": t}
+# turn above symbolic code into exact solution for dolphin and
+# construct the rhs that matches the above exact solution.
+exact_solution_example = hlp.generate_exact_solution_expressions(
+ symbols=symbols,
+ isRichards=isRichards,
+ symbolic_pressure=p_e_sym,
+ symbolic_capillary_pressure=pc_e_sym,
+ saturation_pressure_relationship=S_pc_sym,
+ saturation_pressure_relationship_prime=S_pc_sym_prime,
+ viscosity=viscosity,
+ porosity=porosity,
+ relative_permeability=relative_permeability,
+ relative_permeability_prime=ka_prime,
+ densities=densities,
+ gravity_acceleration=gravity_acceleration,
+ include_gravity=include_gravity,
+ )
+source_expression = exact_solution_example['source']
+exact_solution = exact_solution_example['exact_solution']
+initial_condition = exact_solution_example['initial_condition']
+
+# Dictionary of dirichlet boundary conditions.
+dirichletBC = dict()
+# similarly to the outer boundary dictionary, if a patch has no outer boundary
+# None should be written instead of an expression.
+# This is a bit of a brainfuck:
+# dirichletBC[ind] gives a dictionary of the outer boundaries of subdomain ind.
+# Since a domain patch can have several disjoint outer boundary parts, the
+# expressions need to get an enumaration index which starts at 0.
+# So dirichletBC[ind][j] is the dictionary of outer dirichlet conditions of
+# subdomain ind and boundary part j.
+# Finally, dirichletBC[ind][j]['wetting'] and dirichletBC[ind][j]['nonwetting']
+# return the actual expression needed for the dirichlet condition for both
+# phases if present.
+
+# subdomain index: {outer boudary part index: {phase: expression}}
+for subdomain in isRichards.keys():
+ # if subdomain has no outer boundary, outer_boundary_def_points[subdomain] is None
+ if outer_boundary_def_points[subdomain] is None:
+ dirichletBC.update({subdomain: None})
+ else:
+ dirichletBC.update({subdomain: dict()})
+ # set the dirichlet conditions to be the same code as exact solution on
+ # the subdomain.
+ for outer_boundary_ind in outer_boundary_def_points[subdomain].keys():
+ dirichletBC[subdomain].update(
+ {outer_boundary_ind: exact_solution[subdomain]}
+ )
+
+
+# def saturation(pressure, subdomain_index):
+# # inverse capillary pressure-saturation-relationship
+# return df.conditional(pressure < 0, 1/((1 - pressure)**(1/(subdomain_index + 1))), 1)
+#
+# sa
+for starttime in starttimes:
+ for mesh_resolution, solver_tol in resolutions.items():
+ # initialise LDD simulation class
+ simulation = ldd.LDDsimulation(
+ tol=1E-14,
+ LDDsolver_tol=solver_tol,
+ debug=debugflag,
+ max_iter_num=max_iter_num,
+ FEM_Lagrange_degree=FEM_Lagrange_degree,
+ mesh_study=mesh_study
+ )
+
+ simulation.set_parameters(use_case=use_case,
+ output_dir=output_string,
+ subdomain_def_points=subdomain_def_points,
+ isRichards=isRichards,
+ interface_def_points=interface_def_points,
+ outer_boundary_def_points=outer_boundary_def_points,
+ adjacent_subdomains=adjacent_subdomains,
+ mesh_resolution=mesh_resolution,
+ viscosity=viscosity,
+ porosity=porosity,
+ L=L,
+ lambda_param=lambda_param,
+ relative_permeability=relative_permeability,
+ saturation=sat_pressure_relationship,
+ starttime=starttime,
+ number_of_timesteps=number_of_timesteps,
+ number_of_timesteps_to_analyse=number_of_timesteps_to_analyse,
+ plot_timestep_every=plot_timestep_every,
+ timestep_size=timestep_size,
+ sources=source_expression,
+ initial_conditions=initial_condition,
+ dirichletBC_expression_strings=dirichletBC,
+ exact_solution=exact_solution,
+ densities=densities,
+ include_gravity=include_gravity,
+ write2file=write_to_file,
+ )
+
+ simulation.initialise()
+ output_dir = simulation.output_dir
+ # simulation.write_exact_solution_to_xdmf()
+ output = simulation.run(analyse_condition=analyse_condition)
+ for subdomain_index, subdomain_output in output.items():
+ mesh_h = subdomain_output['mesh_size']
+ for phase, different_errornorms in subdomain_output['errornorm'].items():
+ filename = output_dir + "subdomain{}-space-time-errornorm-{}-phase.csv".format(subdomain_index, phase)
+ # for errortype, errornorm in different_errornorms.items():
+
+ # eocfile = open("eoc_filename", "a")
+ # eocfile.write( str(mesh_h) + " " + str(errornorm) + "\n" )
+ # eocfile.close()
+ # if subdomain.isRichards:mesh_h
+ data_dict = {
+ 'mesh_parameter': mesh_resolution,
+ 'mesh_h': mesh_h,
+ }
+ for error_type, errornorms in different_errornorms.items():
+ data_dict.update(
+ {error_type: errornorms}
+ )
+ errors = pd.DataFrame(data_dict, index=[mesh_resolution])
+ # check if file exists
+ if os.path.isfile(filename) == True:
+ with open(filename, 'a') as f:
+ errors.to_csv(f, header=False, sep='\t', encoding='utf-8', index=False)
+ else:
+ errors.to_csv(filename, sep='\t', encoding='utf-8', index=False)
diff --git a/TP-one-patch/mesh_study_for_fixed_timestep/R-one-patch-mesh-study-fixed-timestep.py b/TP-one-patch/mesh_study_for_fixed_timestep/R-one-patch-mesh-study-fixed-timestep.py
new file mode 100755
index 0000000..14677c9
--- /dev/null
+++ b/TP-one-patch/mesh_study_for_fixed_timestep/R-one-patch-mesh-study-fixed-timestep.py
@@ -0,0 +1,491 @@
+#!/usr/bin/python3
+import dolfin as df
+import mshr
+import numpy as np
+import sympy as sym
+import typing as tp
+import domainPatch as dp
+import LDDsimulation as ldd
+import functools as ft
+import helpers as hlp
+import datetime
+import os
+import pandas as pd
+
+date = datetime.datetime.now()
+datestr = date.strftime("%Y-%m-%d")
+#import ufl as ufl
+
+# init sympy session
+sym.init_printing()
+
+use_case = "R-one-patch-mesh-study-fixed-timestep-new-errornorm"
+# solver_tol = 5E-9
+max_iter_num = 1000
+FEM_Lagrange_degree = 1
+mesh_study = True
+# resolutions = {128: 1e-8} #[1,2,3,4,5,10,20,40,75,100]
+resolutions = {
+ 1: 1e-8,
+ 2: 1e-8,
+ 4: 1e-8,
+ 8: 1e-8,
+ 16: 1e-8,
+ 32: 1e-8,
+ 64: 1e-8,
+ # 128: 1e-8,
+ # 256: 1e-8,
+ # 512: 1e-8,
+ }
+
+############ GRID #######################
+# mesh_resolution = 20
+timestep_size = 0.012
+number_of_timesteps = 1
+plot_timestep_every = 1
+# decide how many timesteps you want analysed. Analysed means, that we write out
+# subsequent errors of the L-iteration within the timestep.
+number_of_timesteps_to_analyse = 1
+starttimes = [0.0]
+# starttimes = [0.0, 0.05]
+
+# starttimes = {
+# 1: 0.0
+# 2: 0.05
+# 4: 0.1
+# 8: 0.2
+# 16: 0.4
+# 32: 0.7
+# 64: 1.0
+# 128: 1.3
+# }
+
+Lw = 0.025 #/timestep_size
+Lnw=Lw
+
+lambda_w = 0
+lambda_nw = 0
+
+include_gravity = False
+debugflag = True
+analyse_condition = False
+
+if mesh_study:
+ output_string = "./output/{}-{}_timesteps{}_P{}".format(datestr, use_case, number_of_timesteps, FEM_Lagrange_degree)
+else:
+ for tol in resolutions.values():
+ solver_tol = tol
+ output_string = "./output/{}-{}_timesteps{}_P{}_solver_tol{}".format(datestr, use_case, number_of_timesteps, FEM_Lagrange_degree, solver_tol)
+
+# toggle what should be written to files
+if mesh_study:
+ write_to_file = {
+ 'space_errornorms': True,
+ 'meshes_and_markers': True,
+ 'L_iterations_per_timestep': True,
+ 'solutions': True,
+ 'absolute_differences': True,
+ 'condition_numbers': analyse_condition,
+ 'subsequent_errors': True
+ }
+else:
+ write_to_file = {
+ 'space_errornorms': True,
+ 'meshes_and_markers': True,
+ 'L_iterations_per_timestep': False,
+ 'solutions': True,
+ 'absolute_differences': True,
+ 'condition_numbers': analyse_condition,
+ 'subsequent_errors': True
+ }
+
+##### Domain and Interface ####
+# global simulation domain domain
+sub_domain0_vertices = [df.Point(-1.0, -1.0), #
+ df.Point(1.0, -1.0), #
+ df.Point(1.0, 1.0), #
+ df.Point(-1.0, 1.0)]
+
+subdomain0_outer_boundary_verts = {
+ 0: [sub_domain0_vertices[0],
+ sub_domain0_vertices[1],
+ sub_domain0_vertices[2],
+ sub_domain0_vertices[3],
+ sub_domain0_vertices[0]]
+}
+
+# list of subdomains given by the boundary polygon vertices.
+# Subdomains are given as a list of dolfin points forming
+# a closed polygon, such that mshr.Polygon(subdomain_def_points[i]) can be used
+# to create the subdomain. subdomain_def_points[0] contains the
+# vertices of the global simulation domain and subdomain_def_points[i] contains the
+# vertices of the subdomain i.
+subdomain_def_points = [sub_domain0_vertices]
+# in the below list, index 0 corresponds to the 12 interface which has index 1
+interface_def_points = None
+
+# if a subdomain has no outer boundary write None instead, i.e.
+# i: None
+# if i is the index of the inner subdomain.
+outer_boundary_def_points = {
+ # subdomain number
+ 0 : subdomain0_outer_boundary_verts
+}
+
+# adjacent_subdomains[i] contains the indices of the subdomains sharing the
+# interface i (i.e. given by interface_def_points[i]).
+adjacent_subdomains = None
+isRichards = {
+ 0: True, #
+ }
+
+viscosity = {#
+# subdom_num : viscosity
+ 0 : {'wetting' :1,
+ 'nonwetting': 1}, #
+}
+
+porosity = {#
+# subdom_num : porosity
+ 0: 1,#
+}
+
+# Dict of the form: { subdom_num : density }
+densities = {
+ 0: {'wetting': 1, #997,
+ 'nonwetting': 1}, #1225}
+}
+
+gravity_acceleration = 9.81
+
+L = {#
+# subdom_num : subdomain L for L-scheme
+ 0: {'wetting' :Lw,
+ 'nonwetting': Lnw},#
+}
+
+lambda_param = {#
+# subdom_num : lambda parameter for the L-scheme
+ 0: {'wetting' :lambda_w,
+ 'nonwetting': lambda_nw},#
+}
+
+## relative permeabilty functions on subdomain 1
+def rel_perm1w(s):
+ # relative permeabilty wetting on subdomain1
+ return s**2
+
+def rel_perm1nw(s):
+ # relative permeabilty nonwetting on subdomain1
+ return (1-s)**2
+
+_rel_perm1w = ft.partial(rel_perm1w)
+_rel_perm1nw = ft.partial(rel_perm1nw)
+
+subdomain1_rel_perm = {
+ 'wetting': _rel_perm1w,#
+ 'nonwetting': _rel_perm1nw
+}
+
+## dictionary of relative permeabilties on all domains.
+relative_permeability = {#
+ 0: subdomain1_rel_perm,
+}
+
+# definition of the derivatives of the relative permeabilities
+# relative permeabilty functions on subdomain 1
+def rel_perm1w_prime(s):
+ # relative permeabilty on subdomain1
+ return 2*s
+
+def rel_perm1nw_prime(s):
+ # relative permeabilty on subdomain1
+ return -2*(1-s)
+
+_rel_perm1w_prime = ft.partial(rel_perm1w_prime)
+_rel_perm1nw_prime = ft.partial(rel_perm1nw_prime)
+
+subdomain1_rel_perm_prime = {
+ 'wetting': _rel_perm1w_prime,
+ 'nonwetting': _rel_perm1nw_prime
+}
+
+# dictionary of relative permeabilties on all domains.
+ka_prime = {
+ 0: subdomain1_rel_perm_prime,
+}
+
+
+
+def saturation(pc, index):
+ # inverse capillary pressure-saturation-relationship
+ return df.conditional(pc > 0, 1/((1 + pc)**(1/(index + 1))), 1)
+
+def saturation_sym(pc, index):
+ # inverse capillary pressure-saturation-relationship
+ return 1/((1 + pc)**(1/(index + 1)))
+
+
+# derivative of S-pc relationship with respect to pc. This is needed for the
+# construction of a analytic solution.
+def saturation_sym_prime(pc, index):
+ # inverse capillary pressure-saturation-relationship
+ return -1/((index+1)*(1 + pc)**((index+2)/(index+1)))
+
+
+# def saturation(pc, index):
+# # inverse capillary pressure-saturation-relationship
+# return df.conditional(pc > 0, -index*pc, 1)
+#
+#
+# def saturation_sym(pc, index):
+# # inverse capillary pressure-saturation-relationship
+# return -index*pc
+#
+#
+# # derivative of S-pc relationship with respect to pc. This is needed for the
+# # construction of a analytic solution.
+# def saturation_sym_prime(pc, index):
+# # inverse capillary pressure-saturation-relationship
+# return -index
+
+
+# note that the conditional definition of S-pc in the nonsymbolic part will be
+# incorporated in the construction of the exact solution below.
+S_pc_sym = {
+ 0: ft.partial(saturation_sym, index=1),
+}
+
+S_pc_sym_prime = {
+ 0: ft.partial(saturation_sym_prime, index=1),
+}
+
+sat_pressure_relationship = {
+ 0: ft.partial(saturation, index=1),
+}
+
+
+#############################################
+# Manufacture source expressions with sympy #
+#############################################
+x, y = sym.symbols('x[0], x[1]') # needed by UFL
+t = sym.symbols('t', positive=True)
+
+epsilon_x_inner = 0.7
+epsilon_x_outer = 0.99
+epsilon_y_inner = epsilon_x_inner
+epsilon_y_outer = epsilon_x_outer
+
+def mollifier(x, epsilon):
+ """ one d mollifier """
+ out_expr = sym.exp(-1/(1-(x/epsilon)**2) + 1)
+ return out_expr
+
+mollifier_handle = ft.partial(mollifier, epsilon=epsilon_x_inner)
+
+pw_sym_x = sym.Piecewise(
+ (mollifier_handle(x), x**2 < epsilon_x_outer**2),
+ (0, True)
+)
+pw_sym_y = sym.Piecewise(
+ (mollifier_handle(y), y**2 < epsilon_y_outer**2),
+ (0, True)
+)
+
+def mollifier2d(x, y, epsilon):
+ """ one d mollifier """
+ out_expr = sym.exp(-1/(1-(x**2 + y**2)/epsilon**2) + 1)
+ return out_expr
+
+mollifier2d_handle = ft.partial(mollifier2d, epsilon=epsilon_x_outer)
+
+pw_sym2d_x = sym.Piecewise(
+ (mollifier2d_handle(x, y), x**2 + y**2 < epsilon_x_outer**2),
+ (0, True)
+)
+
+zero_on_epsilon_shrinking_of_subdomain = sym.Piecewise(
+ (mollifier_handle(sym.sqrt(x**2 + y**2)+2*epsilon_x_inner), ((-2*epsilon_x_inner<sym.sqrt(x**2 + y**2)) & (sym.sqrt(x**2 + y**2)<-epsilon_x_inner))),
+ (0, ((-epsilon_x_inner<=sym.sqrt(x**2 + y**2)) & (sym.sqrt(x**2 + y**2)<=epsilon_x_inner))),
+ (mollifier_handle(sym.sqrt(x**2 + y**2)-2*epsilon_x_inner), ((epsilon_x_inner<sym.sqrt(x**2 + y**2)) & (sym.sqrt(x**2 + y**2)<2*epsilon_x_inner))),
+ (1, True),
+)
+
+zero_on_epsilon_shrinking_of_subdomain_x = sym.Piecewise(
+ (mollifier_handle(x+2*epsilon_x_inner), ((-2*epsilon_x_inner<x) & (x<-epsilon_x_inner))),
+ (0, ((-epsilon_x_inner<=x) & (x<=epsilon_x_inner))),
+ (mollifier_handle(x-2*epsilon_x_inner), ((epsilon_x_inner<x) & (x<2*epsilon_x_inner))),
+ (1, True),
+)
+
+zero_on_epsilon_shrinking_of_subdomain_y = sym.Piecewise(
+ (1, y<=-2*epsilon_x_inner),
+ (mollifier_handle(y+2*epsilon_x_inner), ((-2*epsilon_x_inner<y) & (y<-epsilon_x_inner))),
+ (0, ((-epsilon_x_inner<=y) & (y<=epsilon_x_inner))),
+ (mollifier_handle(y-2*epsilon_x_inner), ((epsilon_x_inner<y) & (y<2*epsilon_x_inner))),
+ (1, True),
+)
+
+zero_on_shrinking = zero_on_epsilon_shrinking_of_subdomain #zero_on_epsilon_shrinking_of_subdomain_x + zero_on_epsilon_shrinking_of_subdomain_y
+gaussian = pw_sym2d_x# pw_sym_y*pw_sym_x
+cutoff = gaussian/(gaussian + zero_on_shrinking)
+
+# # construction of differentiable characteristic function.
+# def smooth_characteristic_func_on_epsilon_shrinking_of_subdomain0(x, y, epsilon_x_inner, epsilon_y_inner, epsilon_x_outer, epsilon_y_outer):
+# dist_to_complement_x = ft.partial(mollifier, epsilon=epsilon_x_inner)
+# dist_to_complement_y = ft.partial(mollifier, epsilon=epsilon_y_inner)
+# dist_to_complement = dist_to_complement_y(y)*dist_to_complement_x(x)
+# dist_to_eps_shrinking_x = ft.partial(zero_outside_epsilon_thickening_of_subdomain, epsilon=epsilon_x_outer)
+# dist_to_eps_shrinking_y = ft.partial(zero_outside_epsilon_thickening_of_subdomain, epsilon=epsilon_y_outer)
+# dist_to_eps_shrinking = dist_to_eps_shrinking_y(y)*dist_to_eps_shrinking_x(x)
+# return dist_to_complement/(dist_to_eps_shrinking + dist_to_complement)
+#
+
+# def dist_to_epsilon_thickening_of_subdomain0_complement(x, y, epsilon):
+# """ calculates the (euklidian distance)^2 of a point x,y to the epsilon
+# thickening of the complement of the domain.
+# """
+# is_inside = ((1-sym.Abs(x) > epsilon) & (1-sym.Abs(y) > epsilon))
+# sym.Piecewise((0, is_inside))
+
+p_e_sym = {
+ 0: {'wetting': (-7 - (1+t*t)*(1 + x*x + y*y)), #*cutoff,
+ 'nonwetting': (-1 -t*(1.1+y + x**2))}, #*cutoff},
+}
+
+pc_e_sym = dict()
+for subdomain, isR in isRichards.items():
+ if isR:
+ pc_e_sym.update({subdomain: -p_e_sym[subdomain]['wetting']})
+ else:
+ pc_e_sym.update({subdomain: p_e_sym[subdomain]['nonwetting']
+ - p_e_sym[subdomain]['wetting']})
+
+
+symbols = {"x": x,
+ "y": y,
+ "t": t}
+# turn above symbolic code into exact solution for dolphin and
+# construct the rhs that matches the above exact solution.
+exact_solution_example = hlp.generate_exact_solution_expressions(
+ symbols=symbols,
+ isRichards=isRichards,
+ symbolic_pressure=p_e_sym,
+ symbolic_capillary_pressure=pc_e_sym,
+ saturation_pressure_relationship=S_pc_sym,
+ saturation_pressure_relationship_prime=S_pc_sym_prime,
+ viscosity=viscosity,
+ porosity=porosity,
+ relative_permeability=relative_permeability,
+ relative_permeability_prime=ka_prime,
+ densities=densities,
+ gravity_acceleration=gravity_acceleration,
+ include_gravity=include_gravity,
+ )
+source_expression = exact_solution_example['source']
+exact_solution = exact_solution_example['exact_solution']
+initial_condition = exact_solution_example['initial_condition']
+
+# Dictionary of dirichlet boundary conditions.
+dirichletBC = dict()
+# similarly to the outer boundary dictionary, if a patch has no outer boundary
+# None should be written instead of an expression.
+# This is a bit of a brainfuck:
+# dirichletBC[ind] gives a dictionary of the outer boundaries of subdomain ind.
+# Since a domain patch can have several disjoint outer boundary parts, the
+# expressions need to get an enumaration index which starts at 0.
+# So dirichletBC[ind][j] is the dictionary of outer dirichlet conditions of
+# subdomain ind and boundary part j.
+# Finally, dirichletBC[ind][j]['wetting'] and dirichletBC[ind][j]['nonwetting']
+# return the actual expression needed for the dirichlet condition for both
+# phases if present.
+
+# subdomain index: {outer boudary part index: {phase: expression}}
+for subdomain in isRichards.keys():
+ # if subdomain has no outer boundary, outer_boundary_def_points[subdomain] is None
+ if outer_boundary_def_points[subdomain] is None:
+ dirichletBC.update({subdomain: None})
+ else:
+ dirichletBC.update({subdomain: dict()})
+ # set the dirichlet conditions to be the same code as exact solution on
+ # the subdomain.
+ for outer_boundary_ind in outer_boundary_def_points[subdomain].keys():
+ dirichletBC[subdomain].update(
+ {outer_boundary_ind: exact_solution[subdomain]}
+ )
+
+
+# def saturation(pressure, subdomain_index):
+# # inverse capillary pressure-saturation-relationship
+# return df.conditional(pressure < 0, 1/((1 - pressure)**(1/(subdomain_index + 1))), 1)
+#
+# sa
+for starttime in starttimes:
+ for mesh_resolution, solver_tol in resolutions.items():
+ # initialise LDD simulation class
+ simulation = ldd.LDDsimulation(
+ tol=1E-14,
+ LDDsolver_tol=solver_tol,
+ debug=debugflag,
+ max_iter_num=max_iter_num,
+ FEM_Lagrange_degree=FEM_Lagrange_degree,
+ mesh_study=mesh_study
+ )
+
+ simulation.set_parameters(use_case=use_case,
+ output_dir=output_string,
+ subdomain_def_points=subdomain_def_points,
+ isRichards=isRichards,
+ interface_def_points=interface_def_points,
+ outer_boundary_def_points=outer_boundary_def_points,
+ adjacent_subdomains=adjacent_subdomains,
+ mesh_resolution=mesh_resolution,
+ viscosity=viscosity,
+ porosity=porosity,
+ L=L,
+ lambda_param=lambda_param,
+ relative_permeability=relative_permeability,
+ saturation=sat_pressure_relationship,
+ starttime=starttime,
+ number_of_timesteps=number_of_timesteps,
+ number_of_timesteps_to_analyse=number_of_timesteps_to_analyse,
+ plot_timestep_every=plot_timestep_every,
+ timestep_size=timestep_size,
+ sources=source_expression,
+ initial_conditions=initial_condition,
+ dirichletBC_expression_strings=dirichletBC,
+ exact_solution=exact_solution,
+ densities=densities,
+ include_gravity=include_gravity,
+ write2file=write_to_file,
+ )
+
+ simulation.initialise()
+ output_dir = simulation.output_dir
+ # simulation.write_exact_solution_to_xdmf()
+ output = simulation.run(analyse_condition=analyse_condition)
+ for subdomain_index, subdomain_output in output.items():
+ mesh_h = subdomain_output['mesh_size']
+ for phase, different_errornorms in subdomain_output['errornorm'].items():
+ filename = output_dir + "subdomain{}-space-time-errornorm-{}-phase.csv".format(subdomain_index, phase)
+ # for errortype, errornorm in different_errornorms.items():
+
+ # eocfile = open("eoc_filename", "a")
+ # eocfile.write( str(mesh_h) + " " + str(errornorm) + "\n" )
+ # eocfile.close()
+ # if subdomain.isRichards:mesh_h
+ data_dict = {
+ 'mesh_parameter': mesh_resolution,
+ 'mesh_h': mesh_h,
+ }
+ for error_type, errornorms in different_errornorms.items():
+ data_dict.update(
+ {error_type: errornorms}
+ )
+ errors = pd.DataFrame(data_dict, index=[mesh_resolution])
+ # check if file exists
+ if os.path.isfile(filename) == True:
+ with open(filename, 'a') as f:
+ errors.to_csv(f, header=False, sep='\t', encoding='utf-8', index=False)
+ else:
+ errors.to_csv(filename, sep='\t', encoding='utf-8', index=False)
diff --git a/TP-one-patch/mesh_study_for_fixed_timestep/TP-one-patch-mesh-study-fixed-timestep-nonwetting0.py b/TP-one-patch/mesh_study_for_fixed_timestep/TP-one-patch-mesh-study-fixed-timestep-nonwetting0.py
index 6135ce9..f15efcf 100755
--- a/TP-one-patch/mesh_study_for_fixed_timestep/TP-one-patch-mesh-study-fixed-timestep-nonwetting0.py
+++ b/TP-one-patch/mesh_study_for_fixed_timestep/TP-one-patch-mesh-study-fixed-timestep-nonwetting0.py
@@ -35,7 +35,7 @@ resolutions = {
64: 1e-10,
128: 1e-10,
256: 1e-10,
- 512: 1e-10,
+ # 512: 1e-10,
}
############ GRID #######################
@@ -46,7 +46,8 @@ plot_timestep_every = 1
# decide how many timesteps you want analysed. Analysed means, that we write out
# subsequent errors of the L-iteration within the timestep.
number_of_timesteps_to_analyse = 1
-starttimes = [0.0, 0.05, 0.1, 0.7, 1.3]
+# starttimes = [0.0, 0.05, 0.1, 0.7, 1.3]
+starttimes = [0.7]
# starttimes = {
# 1: 0.0
diff --git a/TP-one-patch/mesh_study_for_fixed_timestep/TP-one-patch-mesh-study-fixed-timestep-wetting0.py b/TP-one-patch/mesh_study_for_fixed_timestep/TP-one-patch-mesh-study-fixed-timestep-wetting0.py
index b97aa54..9821788 100755
--- a/TP-one-patch/mesh_study_for_fixed_timestep/TP-one-patch-mesh-study-fixed-timestep-wetting0.py
+++ b/TP-one-patch/mesh_study_for_fixed_timestep/TP-one-patch-mesh-study-fixed-timestep-wetting0.py
@@ -19,7 +19,7 @@ datestr = date.strftime("%Y-%m-%d")
# init sympy session
sym.init_printing()
-use_case = "TP-one-patch-mesh-study-fixed-timestep-wetting-constant"
+use_case = "TP-one-patch-mesh-study-fixed-timestep-wetting-constantexi"
# solver_tol = 5E-9
max_iter_num = 2000
FEM_Lagrange_degree = 1
diff --git a/TP-one-patch/mesh_study_for_fixed_timestep/TP-one-patch-mesh-study-fixed-timestep.py b/TP-one-patch/mesh_study_for_fixed_timestep/TP-one-patch-mesh-study-fixed-timestep.py
index 6cd9a7c..5c107d5 100755
--- a/TP-one-patch/mesh_study_for_fixed_timestep/TP-one-patch-mesh-study-fixed-timestep.py
+++ b/TP-one-patch/mesh_study_for_fixed_timestep/TP-one-patch-mesh-study-fixed-timestep.py
@@ -21,26 +21,26 @@ sym.init_printing()
use_case = "TP-one-patch-mesh-study-fixed-timestep"
# solver_tol = 5E-9
-max_iter_num = 2000
+max_iter_num = 1000
FEM_Lagrange_degree = 1
mesh_study = True
# resolutions = {128: 1e-7} #[1,2,3,4,5,10,20,40,75,100]
resolutions = {
- 1: 1e-10,
- 2: 1e-10,
- 4: 1e-10,
- 8: 1e-10,
- 16: 1e-10,
- 32: 1e-10,
- 64: 1e-10,
- 128: 1e-10,
- 256: 1e-10,
- 512: 1e-10,
+ 1: 5e-7,
+ 2: 5e-7,
+ 4: 5e-7,
+ 8: 5e-7,
+ 16: 5e-7,
+ 32: 5e-7,
+ 64: 5e-7,
+ 128: 5e-7,
+ # 256: 1e-10,
+ # 512: 1e-10,
}
############ GRID #######################
# mesh_resolution = 20
-timestep_size = 0.01
+timestep_size = 0.001
number_of_timesteps = 1
plot_timestep_every = 1
# decide how many timesteps you want analysed. Analysed means, that we write out
@@ -59,14 +59,14 @@ starttimes = [0.0, 0.05, 0.1, 0.7, 1.3]
# 128: 1.3
# }
-Lw = 0.05 #/timestep_size
+Lw = 0.025 #/timestep_size
Lnw=Lw
lambda_w = 0
lambda_nw = 0
include_gravity = False
-debugflag = True
+debugflag = False
analyse_condition = False
if mesh_study:
--
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