â€recalculate TPR with scaled densities

Two-phase-Richards/two-patch/TP-R-two-patch-test-case/TP-R-2-realistic-parameters-densities-scaled.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
+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 = "TPR-2-desities-scaled-down"
+# solver_tol = 6E-7
+max_iter_num = 500
+FEM_Lagrange_degree = 1
+mesh_study = False
+resolutions = {
+                # 1: 1e-6,
+                # 2: 1e-6,
+                # 4: 1e-6,
+                # 8: 1e-6,
+                # 16: 1e-6,
+                32: 1e-6,
+                # 64: 1e-6,
+                # 128: 1e-6,
+                # 256: 1e-6,
+                }
+
+############ GRID #######################
+# mesh_resolution = 20
+timestep_size = 0.001
+number_of_timesteps = 1000
+plot_timestep_every = 4
+# 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 = [0.0]
+
+Lw = 0.025 #/timestep_size
+Lnw= 0.025
+
+lambda_w = 40
+lambda_nw = 40
+
+include_gravity = True
+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)]
+# 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]]
+}
+
+# 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: True, #
+    2: False
+    }
+
+
+viscosity = {#
+# subdom_num : viscosity
+    1: {'wetting' :1,
+         'nonwetting': 1/50}, #
+    2: {'wetting' :1,
+         'nonwetting': 1/50}
+}
+
+porosity = {#
+# subdom_num : porosity
+    1: 0.22,#
+    2: 0.0022
+}
+
+# Dict of the form: { subdom_num : density }
+densities = {
+    1: {'wetting': 9.97,
+        'nonwetting': 00.12041},
+    2: {'wetting': 9.97,
+        'nonwetting': 00.12041}
+}
+
+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}
+}
+
+# intrinsic_permeability = {
+#     1: {"wetting": 1,
+#         "nonwetting": 1},
+#     2: {"wetting": 1,
+#         "nonwetting": 1},
+# }
+
+intrinsic_permeability = {
+    1: 1,
+    2: 1,
+}
+
+## relative permeabilty functions on subdomain 1
+def rel_perm1w(s):
+    # relative permeabilty wetting on subdomain1
+    return intrinsic_permeability[1]*s**2
+
+def rel_perm1nw(s):
+    # relative permeabilty nonwetting on subdomain1
+    return intrinsic_permeability[1]*(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 intrinsic_permeability[2]*s**3
+def rel_perm2nw(s):
+    # relative permeabilty nonwetting on subdosym.cos(0.8*t - (0.8*x + 1/7*y))main2
+    return intrinsic_permeability[2]*(1-s)**3
+
+_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 intrinsic_permeability[1]*2*s
+
+def rel_perm1nw_prime(s):
+    # relative permeabilty on subdomain1
+    return -1*intrinsic_permeability[1]*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 subdomain2
+    return intrinsic_permeability[2]*3*s**2
+
+def rel_perm2nw_prime(s):
+    # relative permeabilty on subdomain2
+    return -3*intrinsic_permeability[2]*(1-s)**2
+
+_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 saturation1(pc, subdomain_index):
+#     # inverse capillary pressure-saturation-relationship
+#     return df.conditional(pc > 0, 1/((1 + pc)**(1/(subdomain_index + 1))), 1)
+#
+# def saturation2(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 saturation1_sym(pc, subdomain_index):
+#     # inverse capillary pressure-saturation-relationship
+#     return 1/((1 + pc)**(1/(subdomain_index + 1)))
+#
+#
+# def saturation2_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 saturation1_sym_prime(pc, subdomain_index):
+#     # inverse capillary pressure-saturation-relationship
+#     return -(1/(subdomain_index + 1))*(1 + pc)**((-subdomain_index - 2)/(subdomain_index + 1))
+#
+#
+# def saturation2_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(saturation1_sym, subdomain_index = 1),
+#     2: ft.partial(saturation2_sym, n_index=3, alpha=0.001),
+# }
+#
+# S_pc_sym_prime = {
+#     1: ft.partial(saturation1_sym_prime, subdomain_index = 1),
+#     2: ft.partial(saturation2_sym_prime, n_index=3, alpha=0.001),
+# }
+#
+# sat_pressure_relationship = {
+#     1: ft.partial(saturation1, subdomain_index = 1),#,
+#     2: ft.partial(saturation2, n_index=3, alpha=0.001),
+# }
+
+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)))
+
+
+# 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=2),
+    # 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=2),
+    # 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=2),
+    # 3: ft.partial(saturation, index=2),
+    # 4: 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)
+
+p_e_sym = {
+    1: {'wetting': (-6.0 - (1.0 + t*t)*(1.0 + x*x + y*y))}, #*(1-x)**2*(1+x)**2*(1-y)**2},
+    2: {'wetting': (-6.0 - (1.0 + t*t)*(1.0 + x*x)), #*(1-x)**2*(1+x)**2*(1+y)**2,
+        'nonwetting': (-1-t*(1.1+y + x**2))*y**2}, #*(1-x)**2*(1+x)**2*(1+y)**2},
+} #-y*y*(sym.sin(-2*t+2*x)*sym.sin(1/2*y-1.2*t)) - t*t*x*(0.5-y)*y*(1-x)
+
+
+pc_e_sym = dict()
+for subdomain, isR in isRichards.items():
+    if isR:
+        pc_e_sym.update({subdomain: -p_e_sym[subdomain]['wetting'].copy()})
+    else:
+        pc_e_sym.update({subdomain: p_e_sym[subdomain]['nonwetting'].copy()
+                                        - p_e_sym[subdomain]['wetting'].copy()})
+
+
+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
+
+f = open('TP-R-2-patch-mesh-study.py', 'r')
+print(f.read())
+f.close()
+
+
+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)