From 0e062616d78812fbe7024e77e88994721b2a55c2 Mon Sep 17 00:00:00 2001
From: David Seus <david.seus@ians.uni-stuttgart.de>
Date: Fri, 13 Sep 2019 16:13:12 +0200
Subject: [PATCH] set up one patch mesh study
---
.../mesh_study/TP-one-patch-mesh-study.py | 470 ++++++++++++++++++
1 file changed, 470 insertions(+)
create mode 100755 TP-one-patch/mesh_study/TP-one-patch-mesh-study.py
diff --git a/TP-one-patch/mesh_study/TP-one-patch-mesh-study.py b/TP-one-patch/mesh_study/TP-one-patch-mesh-study.py
new file mode 100755
index 0000000..fe6451e
--- /dev/null
+++ b/TP-one-patch/mesh_study/TP-one-patch-mesh-study.py
@@ -0,0 +1,470 @@
+#!/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 = "TP-one-patch"
+# solver_tol = 5E-9
+max_iter_num = 500
+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: 2e-5,
+ 4: 1e-6,
+ 8: 1e-6,
+ 16: 6e-7,
+ 32: 6e-7,
+ 64: 6e-7,
+ 128: 6e-7}
+
+############ GRID #######################
+# mesh_resolution = 20
+timestep_size = 0.000025
+number_of_timesteps = 4000
+plot_timestep_every = 40
+# 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 = 0.0
+
+Lw = 0.25 #/timestep_size
+Lnw=Lw
+
+lambda_w = 40
+lambda_nw = 40
+
+include_gravity = False
+debugflag = False
+analyse_condition = False
+
+output_string = "./output/{}-{}_timesteps{}_P{}".format(datestr, use_case, number_of_timesteps, FEM_Lagrange_degree)
+
+# toggle what should be written to files
+if mesh_study:
+ write_to_file = {
+ 'space_errornorms': True,
+ 'meshes_and_markers': True,
+ 'L_iterations_per_timestep': False,
+ 'solutions': True,
+ 'absolute_differences': False,
+ '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: False, #
+ }
+
+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 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)
--
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