diff --git a/TP-TP-patch-test-case/TP-TP-2-patch-test.py b/TP-TP-patch-test-case/TP-TP-2-patch-test.py
new file mode 100755
index 0000000000000000000000000000000000000000..48c98029c124e28735e3684325eb3c495e98fbf4
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+++ b/TP-TP-patch-test-case/TP-TP-2-patch-test.py
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+#!/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 ufl as ufl
+
+# init sympy session
+sym.init_printing()
+
+##### Domain and Interface ####
+# global simulation domain domain
+sub_domain0_vertices = [df.Point(0.0,0.0), #
+ df.Point(1.0,0.0),#
+ df.Point(1.0,1.0),#
+ df.Point(0.0,1.0)]
+# interface between subdomain1 and subdomain2
+interface12_vertices = [df.Point(0.0, 0.5),
+ df.Point(1.0, 0.5) ]
+# subdomain1.
+sub_domain1_vertices = [interface12_vertices[0],
+ interface12_vertices[1],
+ df.Point(1.0,1.0),
+ df.Point(0.0,1.0) ]
+
+# 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[0], #
+ df.Point(0.0,1.0), #
+ df.Point(1.0,1.0), #
+ interface12_vertices[1]]
+}
+# subdomain2
+sub_domain2_vertices = [df.Point(0.0,0.0),
+ df.Point(1.0,0.0),
+ interface12_vertices[1],
+ interface12_vertices[0] ]
+
+subdomain2_outer_boundary_verts = {
+ 0: [interface12_vertices[1], #
+ df.Point(1.0,0.0), #
+ df.Point(0.0,0.0), #
+ interface12_vertices[0]]
+}
+# 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
+ }
+
+
+############ GRID ########################ΓΌ
+mesh_resolution = 40
+timestep_size = 5*0.0001
+number_of_timesteps = 1000
+# 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 = 11
+starttime = 0
+
+viscosity = {#
+# subdom_num : viscosity
+ 1 : {'wetting' :1,
+ 'nonwetting': 1/50}, #
+ 2 : {'wetting' :1,
+ 'nonwetting': 1/50}
+}
+
+porosity = {#
+# subdom_num : porosity
+ 1 : 1,#
+ 2 : 1
+}
+
+L = {#
+# subdom_num : subdomain L for L-scheme
+ 1 : {'wetting' :0.25,
+ 'nonwetting': 0.25},#
+ 2 : {'wetting' :0.25,
+ 'nonwetting': 0.25}
+}
+
+lambda_param = {#
+# subdom_num : lambda parameter for the L-scheme
+ 1 : {'wetting' :20,
+ 'nonwetting': 35},#
+ 2 : {'wetting' :20,
+ 'nonwetting': 35}
+}
+
+## 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)**3
+
+_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**3
+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
+}
+
+# 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(capillary_pressure, n_index, alpha):
+ # inverse capillary pressure-saturation-relationship
+ return df.conditional(capillary_pressure > 0, 1/((1 + (alpha*capillary_pressure)**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(capillary_pressure, n_index, alpha):
+ # inverse capillary pressure-saturation-relationship
+ #df.conditional(capillary_pressure > 0,
+ return 1/((1 + (alpha*capillary_pressure)**n_index)**((n_index - 1)/n_index))
+
+S_pc_rel = {#
+ 1: ft.partial(saturation_sym, n_index = 3, alpha=0.001),# n= 3 stands for non-uniform porous media
+ 2: ft.partial(saturation_sym, n_index = 6, alpha=0.001) # n=6 stands for uniform porous media matrix (siehe Helmig)
+}
+
+S_pc_rel_sym = {#
+ 1: ft.partial(saturation_sym, n_index = sym.Symbol('n'), alpha = sym.Symbol('a')),# n= 3 stands for non-uniform porous media
+ 2: ft.partial(saturation_sym, n_index = sym.Symbol('n'), alpha = sym.Symbol('a')) # n=6 stands for uniform porous media matrix (siehe Helmig)
+}
+
+#### Manufacture source expressions with sympy
+###############################################################################
+## subdomain1
+x, y = sym.symbols('x[0], x[1]') # needed by UFL
+t = sym.symbols('t', positive=True)
+#f = -sym.diff(u, x, 2) - sym.diff(u, y, 2) # -Laplace(u)
+#f = sym.simplify(f) # simplify f
+p1_w = 1 - (1+t**2)*(1 + x**2 + (y-0.5)**2)
+p1_nw = t*(1-(y-0.5) - x**2)**2 - sym.sqrt(2+t**2)*(1-(y-0.5))
+
+#dtS1_w = sym.diff(S_pc_rel_sym[1](p1_nw - p1_w), t, 1)
+#dtS1_nw = -sym.diff(S_pc_rel_sym[1](p1_nw - p1_w), t, 1)
+dtS1_w = porosity[1]*sym.diff(S_pc_rel[1](p1_nw - p1_w), t, 1)
+dtS1_nw = -porosity[1]*sym.diff(S_pc_rel[1](p1_nw - p1_w), t, 1)
+print("dtS1_w = ", dtS1_w, "\n")
+print("dtS1_nw = ", dtS1_nw, "\n")
+
+#dxdxflux1_w = -sym.diff(relative_permeability[1]['wetting'](S_pc_rel_sym[1](p1_nw - p1_w))*sym.diff(p1_w, x, 1), x, 1)
+#dydyflux1_w = -sym.diff(relative_permeability[1]['wetting'](S_pc_rel_sym[1](p1_nw - p1_w))*sym.diff(p1_w, y, 1), y, 1)
+dxdxflux1_w = -1/viscosity[1]['wetting']*sym.diff(relative_permeability[1]['wetting'](S_pc_rel[1](p1_nw - p1_w))*sym.diff(p1_w, x, 1), x, 1)
+dydyflux1_w = -1/viscosity[1]['wetting']*sym.diff(relative_permeability[1]['wetting'](S_pc_rel[1](p1_nw - p1_w))*sym.diff(p1_w, y, 1), y, 1)
+
+rhs1_w = dtS1_w + dxdxflux1_w + dydyflux1_w
+rhs1_w = sym.printing.ccode(rhs1_w)
+print("rhs_w = ", rhs1_w, "\n")
+#rhs_w = sym.expand(rhs_w)
+#print("rhs_w", rhs_w, "\n")
+#rhs_w = sym.collect(rhs_w, x)
+#print("rhs_w", rhs_w, "\n")
+
+#dxdxflux1_nw = -sym.diff(relative_permeability[1]['nonwetting'](S_pc_rel_sym[1](p1_nw - p1_w))*sym.diff(p1_nw, x, 1), x, 1)
+#dydyflux1_nw = -sym.diff(relative_permeability[1]['nonwetting'](S_pc_rel_sym[1](p1_nw - p1_w))*sym.diff(p1_nw, y, 1), y, 1)
+dxdxflux1_nw = -1/viscosity[1]['nonwetting']*sym.diff(relative_permeability[1]['nonwetting'](1-S_pc_rel[1](p1_nw - p1_w))*sym.diff(p1_nw, x, 1), x, 1)
+dydyflux1_nw = -1/viscosity[1]['nonwetting']*sym.diff(relative_permeability[1]['nonwetting'](1-S_pc_rel[1](p1_nw - p1_w))*sym.diff(p1_nw, y, 1), y, 1)
+
+rhs1_nw = dtS1_nw + dxdxflux1_nw + dydyflux1_nw
+rhs1_nw = sym.printing.ccode(rhs1_nw)
+print("rhs_nw = ", rhs1_nw, "\n")
+
+## subdomain2
+p2_w = 1 - (1+t**2)*(1 + x**2)
+p2_nw = t*(1- x**2)**2 - sym.sqrt(2+t**2)*(1-(y-0.5))
+
+#dtS2_w = sym.diff(S_pc_rel_sym[2](p2_nw - p2_w), t, 1)
+#dtS2_nw = -sym.diff(S_pc_rel_sym[2](p2_nw - p2_w), t, 1)
+dtS2_w = porosity[2]*sym.diff(S_pc_rel[2](p2_nw - p2_w), t, 1)
+dtS2_nw = -porosity[2]*sym.diff(S_pc_rel[2](p2_nw - p2_w), t, 1)
+print("dtS2_w = ", dtS2_w, "\n")
+print("dtS2_nw = ", dtS2_nw, "\n")
+
+#dxdxflux2_w = -sym.diff(relative_permeability[2]['wetting'](S_pc_rel_sym[2](p2_nw - p2_w))*sym.diff(p2_w, x, 1), x, 1)
+#dydyflux2_w = -sym.diff(relative_permeability[2]['wetting'](S_pc_rel_sym[2](p2_nw - p2_w))*sym.diff(p2_w, y, 1), y, 1)
+dxdxflux2_w = -1/viscosity[2]['wetting']*sym.diff(relative_permeability[2]['wetting'](S_pc_rel[2](p2_nw - p2_w))*sym.diff(p2_w, x, 1), x, 1)
+dydyflux2_w = -1/viscosity[2]['wetting']*sym.diff(relative_permeability[2]['wetting'](S_pc_rel[2](p2_nw - p2_w))*sym.diff(p2_w, y, 1), y, 1)
+
+rhs2_w = dtS2_w + dxdxflux2_w + dydyflux2_w
+rhs2_w = sym.printing.ccode(rhs2_w)
+print("rhs2_w = ", rhs2_w, "\n")
+#rhs_w = sym.expand(rhs_w)
+#print("rhs_w", rhs_w, "\n")
+#rhs_w = sym.collect(rhs_w, x)
+#print("rhs_w", rhs_w, "\n")
+
+#dxdxflux2_nw = -sym.diff(relative_permeability[2]['nonwetting'](S_pc_rel_sym[2](p2_nw - p2_w))*sym.diff(p2_nw, x, 1), x, 1)
+#dydyflux2_nw = -sym.diff(relative_permeability[2]['nonwetting'](S_pc_rel_sym[2](p2_nw - p2_w))*sym.diff(p2_nw, y, 1), y, 1)
+dxdxflux2_nw = -1/viscosity[2]['nonwetting']*sym.diff(relative_permeability[2]['nonwetting'](1-S_pc_rel[2](p2_nw - p2_w))*sym.diff(p2_nw, x, 1), x, 1)
+dydyflux2_nw = -1/viscosity[2]['nonwetting']*sym.diff(relative_permeability[2]['nonwetting'](1-S_pc_rel[2](p2_nw - p2_w))*sym.diff(p2_nw, y, 1), y, 1)
+
+rhs2_nw = dtS2_nw + dxdxflux2_nw + dydyflux2_nw
+rhs2_nw = sym.printing.ccode(rhs2_nw)
+print("rhs2_nw = ", rhs2_nw, "\n")
+
+
+###############################################################################
+
+source_expression = {
+ 1: {'wetting': rhs1_w,
+ 'nonwetting': rhs1_nw},
+ 2: {'wetting': rhs2_w,
+ 'nonwetting': rhs2_nw}
+}
+
+p1_w_00 = p1_w.subs(t, 0)
+p1_nw_00 = p1_nw.subs(t, 0)
+p2_w_00 = p2_w.subs(t, 0)
+p2_nw_00 = p2_nw.subs(t, 0)
+# p1_w_00 = sym.printing.ccode(p1_w_00)
+
+initial_condition = {
+ 1: {'wetting': sym.printing.ccode(p1_w_00),
+ 'nonwetting': sym.printing.ccode(p1_nw_00)},#
+ 2: {'wetting': sym.printing.ccode(p2_w_00),
+ 'nonwetting': sym.printing.ccode(p2_nw_00)}
+}
+
+exact_solution = {
+ 1: {'wetting': sym.printing.ccode(p1_w),
+ 'nonwetting': sym.printing.ccode(p1_nw)},#
+ 2: {'wetting': sym.printing.ccode(p2_w),
+ 'nonwetting': sym.printing.ccode(p2_nw)}
+}
+
+# similary 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.
+dirichletBC = {
+#subdomain index: {outer boudary part index: {phase: expression}}
+ 1: { 0: {'wetting': sym.printing.ccode(p1_w),
+ 'nonwetting': sym.printing.ccode(p1_nw)}},
+ 2: { 0: {'wetting': sym.printing.ccode(p2_w),
+ 'nonwetting': sym.printing.ccode(p2_nw)}}
+}
+
+# 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
+}
+
+
+# initialise LDD simulation class
+simulation = ldd.LDDsimulation(tol = 1E-14, debug = False)
+simulation.set_parameters(output_dir = "./output/",#
+ 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 = S_pc_rel,#
+ 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,#
+ write2file = write_to_file,#
+ )
+
+simulation.initialise()
+# simulation.write_exact_solution_to_xdmf()
+simulation.run()