add mesh study example

TP-TP-2-patch-pure-dd-avoid-interface-at-origin/mesh_study_convergence/TP-TP-2-patch-pure-dd-convergence-study.py

+#!/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
+
+date = datetime.datetime.now()
+datestr = date.strftime("%Y-%m-%d")
+#import ufl as ufl
+
+# init sympy session
+sym.init_printing()
+
+use_case = "TP-TP-2-patch-pure-dd"
+solver_tol = 6E-7
+max_iter_num = 1000
+FEM_Lagrange_degree = 1
+
+############ GRID #######################
+# mesh_resolution = 20
+timestep_size = 0.0001
+number_of_timesteps = 1000
+plot_timestep_every = 10
+# 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 = 0
+starttime = 0
+
+Lw = 0.25 #/timestep_size
+Lnw=Lw
+
+lambda_w = 40
+lambda_nw = 40
+
+include_gravity = False
+debugflag = False
+analyse_condition = True
+
+output_string = "./output/{}-{}_timesteps{}_P{}-solver_tol{}".format(datestr, use_case, number_of_timesteps, FEM_Lagrange_degree, solver_tol)
+
+##### 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)]
+# interface between subdomain1 and subdomain2
+interface12_vertices = [df.Point(-1.0, 0.0),
+                        df.Point(1.0, 0.0) ]
+# subdomain1.
+sub_domain1_vertices = [interface12_vertices[0],
+                        interface12_vertices[1],
+                        sub_domain0_vertices[2],
+                        sub_domain0_vertices[3] ]
+
+# vertex coordinates of the outer boundaries. If it can not be specified as a
+# polygon, use an entry per boundary polygon. This information is used for defining
+# the Dirichlet boundary conditions. If a domain is completely internal, the
+# dictionary entry should be 0: None
+subdomain1_outer_boundary_verts = {
+    0: [interface12_vertices[1],
+        sub_domain0_vertices[2],
+        sub_domain0_vertices[3], #
+        interface12_vertices[0]]
+}
+# subdomain2
+sub_domain2_vertices = [sub_domain0_vertices[0],
+                        sub_domain0_vertices[1],
+                        interface12_vertices[1],
+                        interface12_vertices[0] ]
+
+subdomain2_outer_boundary_verts = {
+    0: [interface12_vertices[0], #
+        sub_domain0_vertices[0],
+        sub_domain0_vertices[1],
+        interface12_vertices[1]]
+}
+# subdomain2_outer_boundary_verts = {
+#     0: [interface12_vertices[0], df.Point(0.0,0.0)],#
+#     1: [df.Point(0.0,0.0), df.Point(1.0,0.0)], #
+#     2: [df.Point(1.0,0.0), interface12_vertices[1]]
+# }
+# subdomain2_outer_boundary_verts = {
+#     0: None
+# }
+
+# 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,#
+                      sub_domain1_vertices,#
+                      sub_domain2_vertices]
+# in the below list, index 0 corresponds to the 12 interface which has index 1
+interface_def_points = [interface12_vertices]
+
+# 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
+    1 : subdomain1_outer_boundary_verts,
+    2 : subdomain2_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 = [[1,2]]
+isRichards = {
+    1: False, #
+    2: False
+    }
+
+
+viscosity = {#
+# subdom_num : viscosity
+    1 : {'wetting' :1,
+         'nonwetting': 1}, #
+    2 : {'wetting' :1,
+         'nonwetting': 1}
+}
+
+porosity = {#
+# subdom_num : porosity
+    1 : 1,#
+    2 : 1
+}
+
+# Dict of the form: { subdom_num : density }
+densities = {
+    1: {'wetting': 1,  #997,
+        'nonwetting': 1}, #1225},
+    2: {'wetting': 1,  #997,
+        'nonwetting': 1}, #1225},
+}
+
+gravity_acceleration = 9.81
+
+
+L = {#
+# subdom_num : subdomain L for L-scheme
+    1 : {'wetting' :Lw,
+         'nonwetting': Lnw},#
+    2 : {'wetting' :Lw,
+         'nonwetting': Lnw}
+}
+
+
+lambda_param = {#
+# subdom_num : lambda parameter for the L-scheme
+    1 : {'wetting' :lambda_w,
+         'nonwetting': lambda_nw},#
+    2 : {'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
+}
+## relative permeabilty functions on subdomain 2
+def rel_perm2w(s):
+    # relative permeabilty wetting on subdomain2
+    return s**2
+def rel_perm2nw(s):
+    # relative permeabilty nonwetting on subdosym.cos(0.8*t - (0.8*x + 1/7*y))main2
+    return (1-s)**2
+
+_rel_perm2w = ft.partial(rel_perm2w)
+_rel_perm2nw = ft.partial(rel_perm2nw)
+
+subdomain2_rel_perm = {
+    'wetting': _rel_perm2w,#
+    'nonwetting': _rel_perm2nw
+}
+
+## dictionary of relative permeabilties on all domains.
+relative_permeability = {#
+    1: subdomain1_rel_perm,
+    2: subdomain2_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)
+
+# # definition of the derivatives of the relative permeabilities
+# # relative permeabilty functions on subdomain 1
+def rel_perm2w_prime(s):
+    # relative permeabilty on subdomain1
+    return 2*s
+
+def rel_perm2nw_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)
+_rel_perm2w_prime = ft.partial(rel_perm2w_prime)
+_rel_perm2nw_prime = ft.partial(rel_perm2nw_prime)
+
+subdomain1_rel_perm_prime = {
+    'wetting': _rel_perm1w_prime,
+    'nonwetting': _rel_perm1nw_prime
+}
+
+
+subdomain2_rel_perm_prime = {
+    'wetting': _rel_perm2w_prime,
+    'nonwetting': _rel_perm2nw_prime
+}
+
+# dictionary of relative permeabilties on all domains.
+ka_prime = {
+    1: subdomain1_rel_perm_prime,
+    2: subdomain2_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 pc_sat_rel_sym(S, index):
+    # capillary pressure-saturation-relationship
+    return 1/S**(index+1) -1
+
+pc_saturation_sym = {
+    1: ft.partial(pc_sat_rel_sym, index=1),
+    2: ft.partial(pc_sat_rel_sym, index=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)))
+
+
+# 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 = {
+    1: ft.partial(saturation_sym, index=1),
+    2: ft.partial(saturation_sym, index=1),
+    # 3: ft.partial(saturation_sym, index=2),
+    # 4: ft.partial(saturation_sym, index=1)
+}
+
+S_pc_sym_prime = {
+    1: ft.partial(saturation_sym_prime, index=1),
+    2: ft.partial(saturation_sym_prime, index=1),
+    # 3: ft.partial(saturation_sym_prime, index=2),
+    # 4: ft.partial(saturation_sym_prime, index=1)
+}
+
+sat_pressure_relationship = {
+    1: ft.partial(saturation, index=1),
+    2: ft.partial(saturation, index=1),
+    # 3: ft.partial(saturation, index=2),
+    # 4: ft.partial(saturation, index=1)
+}
+
+#
+# def saturation(pc, n_index, alpha):
+#     # inverse capillary pressure-saturation-relationship
+#     return df.conditional(pc > 0, 1/((1 + (alpha*pc)**n_index)**((n_index - 1)/n_index)), 1)
+#
+# # S-pc-relation ship. We use the van Genuchten approach, i.e. pc = 1/alpha*(S^{-1/m} -1)^1/n, where
+# # we set alpha = 0, assume m = 1-1/n (see Helmig) and assume that residual saturation is Sw
+# def saturation_sym(pc, n_index, alpha):
+#     # inverse capillary pressure-saturation-relationship
+#     #df.conditional(pc > 0,
+#     return 1/((1 + (alpha*pc)**n_index)**((n_index - 1)/n_index))
+#
+#
+# # derivative of S-pc relationship with respect to pc. This is needed for the
+# # construction of a analytic solution.
+# def saturation_sym_prime(pc, n_index, alpha):
+#     # inverse capillary pressure-saturation-relationship
+#     return -(alpha*(n_index - 1)*(alpha*pc)**(n_index - 1)) / ( (1 + (alpha*pc)**n_index)**((2*n_index - 1)/n_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 = {
+#     1: ft.partial(saturation_sym, n_index=3, alpha=0.001),
+#     2: ft.partial(saturation_sym, n_index=6, alpha=0.001),
+#     # 3: ft.partial(saturation_sym, n_index=3, alpha=0.001),
+#     # 4: ft.partial(saturation_sym, n_index=3, alpha=0.001),
+#     # 5: ft.partial(saturation_sym, n_index=3, alpha=0.001),
+#     # 6: ft.partial(saturation_sym, n_index=3, alpha=0.001)
+# }
+#
+# S_pc_sym_prime = {
+#     1: ft.partial(saturation_sym_prime, n_index=3, alpha=0.001),
+#     2: ft.partial(saturation_sym_prime, n_index=6, alpha=0.001),
+#     # 3: ft.partial(saturation_sym_prime, n_index=3, alpha=0.001),
+#     # 4: ft.partial(saturation_sym_prime, n_index=3, alpha=0.001),
+#     # 5: ft.partial(saturation_sym_prime, n_index=3, alpha=0.001),
+#     # 6: ft.partial(saturation_sym_prime, n_index=3, alpha=0.001)
+# }
+#
+# sat_pressure_relationship = {
+#     1: ft.partial(saturation, n_index=3, alpha=0.001),
+#     2: ft.partial(saturation, n_index=6, alpha=0.001),p1w + Spc[1]
+#     # 3: ft.partial(saturation, n_index=3, alpha=0.001),
+#     # 4: ft.partial(saturation, n_index=3, alpha=0.001),
+#     # 5: ft.partial(saturation, n_index=3, alpha=0.001),
+#     # 6: ft.partial(saturation, n_index=3, alpha=0.001)
+# }
+#
+
+
+#############################################
+# Manufacture source expressions with sympy #
+#############################################
+x, y = sym.symbols('x[0], x[1]')  # needed by UFL
+t = sym.symbols('t', positive=True)
+
+symbols = { "x": x,
+            "y": y,
+            "t": t}
+
+# 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)
+#
+#
+# sat_sym = {
+#     1: 0.5 + 0.25*sym.sin(x-t)*sym.cos(y-t),
+#     2: 0.5 + 0.25*sym.sin(x-t)*sym.cos(y-t)
+#     }
+#
+# Spc = {
+#     1: sym.Piecewise((pc_saturation_sym[1](sat_sym[1]), sat_sym[1] > 0), (pc_saturation_sym[1](sat_sym[1]), 1>=sat_sym[1]), (0, True)),
+#     2: sym.Piecewise((pc_saturation_sym[2](sat_sym[2]), sat_sym[2] > 0), (pc_saturation_sym[2](sat_sym[2]), 2>=sat_sym[2]), (0, True))
+#     }
+#
+# p1w = (-1 - (1+t*t)*(1 + x*x + y*y))#*cutoff
+# p2w = p1w
+# p_e_sym = {
+#     1: {'wetting': p1w,
+#         'nonwetting': (p1w + Spc[1])}, #*cutoff},
+#     2: {'wetting': p2w,
+#         'nonwetting': (p2w + Spc[2])}, #*cutoff},
+# }
+
+p_e_sym = {
+    1: {'wetting': (-6 - (1+t*t)*(1 + x*x + y*y)),  #*cutoff,
+        'nonwetting': (-1 -t*(1.1+ y + x**2))},  #*(sym.sin((1+y)/2*sym.pi)*sym.sin((1+x)/2*sym.pi))**2},
+    2: {'wetting': (-6 - (1+t*t)*(1 + x*x + y*y)),  #*(sym.sin((1+y)/2*sym.pi)*sym.sin((1+x)/2*sym.pi))**2,
+        'nonwetting': (-1 -t*(1.1+ y + x**2))},  #*(sym.sin((1+y)/2*sym.pi)*sym.sin((1+x)/2*sym.pi))**2},
+    # 1: {'wetting': (-5 - (1+t*t)*(1 + x*x + y*y)),  #*cutoff,
+    #     'nonwetting': (-1 -t*(1.1+y + x**2))},  #*cutoff},
+    # 2: {'wetting': (-5 - (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']})
+
+
+
+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
+
+write_to_file = {
+    'meshes_and_markers': True,
+    'L_iterations': True,
+    'solutions': False,
+    'absolute_differences': False,
+    'condition_numbers': False,
+    'subsequent_errors': False
+}
+
+
+# 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,
+    plot_timestep_every=plot_timestep_every
+    )
+
+resolutions = [5, 10, 15] #, 20, 25, 30, 35, 40, 45, 50]
+
+for mesh_resolution in resolutions:
+    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,
+                              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()
+    # simulation.write_exact_solution_to_xdmf()
+    simulation.run(analyse_condition=analyse_condition)