diff --git a/TP-TP-layered-soil-case/mesh_study/TP-TP-layered_soil_pure_dd_mesh_study.py b/TP-TP-layered-soil-case/mesh_study/TP-TP-layered_soil_pure_dd_mesh_study.py
new file mode 100755
index 0000000000000000000000000000000000000000..c2b5bf6214a3e8fc96ec4ca77419c873759722ec
--- /dev/null
+++ b/TP-TP-layered-soil-case/mesh_study/TP-TP-layered_soil_pure_dd_mesh_study.py
@@ -0,0 +1,614 @@
+#!/usr/bin/python3
+"""This program sets up a domain together with a decomposition into subdomains
+modelling layered soil. This is used for our LDD article with tp-tp and tp-r
+coupling.
+
+Along with the subdomains and the mesh domain markers are set upself.
+The resulting mesh is saved into files for later use.
+"""
+
+#!/usr/bin/python3
+import dolfin as df
+import mshr
+import numpy as np
+import sympy as sym
+import typing as tp
+import functools as ft
+import domainPatch as dp
+import LDDsimulation as ldd
+import helpers as hlp
+import datetime
+import os
+import pandas as pd
+
+date = datetime.datetime.now()
+datestr = date.strftime("%Y-%m-%d")
+
+# init sympy session
+sym.init_printing()
+# solver_tol = 6E-7
+use_case = "TP-TP-layered-soil-pure-dd"
+max_iter_num = 1000
+FEM_Lagrange_degree = 1
+mesh_study = True
+resolutions = {
+ # 1: 1e-7, # h=2
+ 2: 1e-7, # h=1.1180
+ 4: 1e-7, # h=0.5590
+ 8: 1e-7, # h=0.2814
+ 16: 1e-7, # h=0.1412
+ 32: 1e-7, # h=0.0706
+ 64: 1e-7,
+ 128: 1e-7,
+ 256: 1e-7
+ }
+
+############ GRID #######################
+# mesh_resolution = 20
+timestep_size = 0.0025
+number_of_timesteps = 300
+plot_timestep_every = 2
+# 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
+starttimes = [0.0, 0.25, 0.5]
+
+Lw = 0.025 #/timestep_size
+Lnw=Lw
+
+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': False,
+ 'solutions': False,
+ 'absolute_differences': False,
+ 'condition_numbers': analyse_condition,
+ 'subsequent_errors': False
+ }
+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
+ }
+
+# global domain
+subdomain0_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)]
+
+interface12_vertices = [df.Point(-1.0, 0.8),
+ df.Point(0.3, 0.8),
+ df.Point(0.5, 0.9),
+ df.Point(0.8, 0.7),
+ df.Point(1.0, 0.65)]
+# subdomain1.
+subdomain1_vertices = [interface12_vertices[0],
+ interface12_vertices[1],
+ interface12_vertices[2],
+ interface12_vertices[3],
+ interface12_vertices[4], # southern boundary, 12 interface
+ subdomain0_vertices[2], # eastern boundary, outer boundary
+ subdomain0_vertices[3]] # northern boundary, outer on_boundary
+
+# 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[4], #
+ subdomain0_vertices[2], # eastern boundary, outer boundary
+ subdomain0_vertices[3],
+ interface12_vertices[0]]
+}
+
+
+# interface23
+interface23_vertices = [df.Point(-1.0, 0.0),
+ df.Point(-0.35, 0.0),
+ # df.Point(6.5, 4.5),
+ df.Point(0.0, 0.0),
+ df.Point(0.5, 0.0),
+ # df.Point(11.5, 3.5),
+ # df.Point(13.0, 3)
+ df.Point(0.85, 0.0),
+ df.Point(1.0, 0.0)
+ ]
+
+#subdomain1
+subdomain2_vertices = [interface23_vertices[0],
+ interface23_vertices[1],
+ interface23_vertices[2],
+ interface23_vertices[3],
+ interface23_vertices[4],
+ interface23_vertices[5], # southern boundary, 23 interface
+ subdomain1_vertices[4], # eastern boundary, outer boundary
+ subdomain1_vertices[3],
+ subdomain1_vertices[2],
+ subdomain1_vertices[1],
+ subdomain1_vertices[0] ] # northern boundary, 12 interface
+
+subdomain2_outer_boundary_verts = {
+ 0: [interface23_vertices[5],
+ subdomain1_vertices[4]],
+ 1: [subdomain1_vertices[0],
+ interface23_vertices[0]]
+}
+
+
+# interface34
+interface34_vertices = [df.Point(-1.0, -0.6),
+ df.Point(-0.6, -0.45),
+ df.Point(0.3, -0.25),
+ df.Point(0.65, -0.6),
+ df.Point(1.0, -0.7)]
+
+# subdomain3
+subdomain3_vertices = [interface34_vertices[0],
+ interface34_vertices[1],
+ interface34_vertices[2],
+ interface34_vertices[3],
+ interface34_vertices[4], # southern boundary, 34 interface
+ subdomain2_vertices[5], # eastern boundary, outer boundary
+ subdomain2_vertices[4],
+ subdomain2_vertices[3],
+ subdomain2_vertices[2],
+ subdomain2_vertices[1],
+ subdomain2_vertices[0] ] # northern boundary, 23 interface
+
+subdomain3_outer_boundary_verts = {
+ 0: [interface34_vertices[4],
+ subdomain2_vertices[5]],
+ 1: [subdomain2_vertices[0],
+ interface34_vertices[0]]
+}
+
+# subdomain4
+subdomain4_vertices = [subdomain0_vertices[0],
+ subdomain0_vertices[1], # southern boundary, outer boundary
+ subdomain3_vertices[4],# eastern boundary, outer boundary
+ subdomain3_vertices[3],
+ subdomain3_vertices[2],
+ subdomain3_vertices[1],
+ subdomain3_vertices[0] ] # northern boundary, 34 interface
+
+subdomain4_outer_boundary_verts = {
+ 0: [subdomain4_vertices[6],
+ subdomain4_vertices[0],
+ subdomain4_vertices[1],
+ subdomain4_vertices[2]]
+}
+
+
+subdomain_def_points = [subdomain0_vertices,#
+ subdomain1_vertices,#
+ subdomain2_vertices,#
+ subdomain3_vertices,#
+ subdomain4_vertices
+ ]
+
+
+# interface_vertices introduces a global numbering of interfaces.
+interface_def_points = [interface12_vertices, interface23_vertices, interface34_vertices]
+adjacent_subdomains = [[1,2], [2,3], [3,4]]
+
+# 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,
+ 3: subdomain3_outer_boundary_verts,
+ 4: subdomain4_outer_boundary_verts
+}
+
+isRichards = {
+ 1: False,
+ 2: False,
+ 3: False,
+ 4: False
+ }
+
+# isRichards = {
+# 1: True,
+# 2: True,
+# 3: True,
+# 4: True
+# }
+
+# Dict of the form: { subdom_num : viscosity }
+viscosity = {
+ 1: {'wetting' :1,
+ 'nonwetting': 1},
+ 2: {'wetting' :1,
+ 'nonwetting': 1},
+ 3: {'wetting' :1,
+ 'nonwetting': 1},
+ 4: {'wetting' :1,
+ 'nonwetting': 1},
+}
+
+# Dict of the form: { subdom_num : density }
+densities = {
+ 1: {'wetting': 1, #997
+ 'nonwetting':1}, #1.225}},
+ 2: {'wetting': 1, #997
+ 'nonwetting':1}, #1.225}},
+ 3: {'wetting': 1, #997
+ 'nonwetting':1}, #1.225}},
+ 4: {'wetting': 1, #997
+ 'nonwetting':1}, #1.225}}
+}
+
+gravity_acceleration = 9.81
+# porosities taken from
+# https://www.geotechdata.info/parameter/soil-porosity.html
+# Dict of the form: { subdom_num : porosity }
+porosity = {
+ 1: 1, #0.2, # Clayey gravels, clayey sandy gravels
+ 2: 1, #0.22, # Silty gravels, silty sandy gravels
+ 3: 1, #0.37, # Clayey sands
+ 4: 1, #0.2 # Silty or sandy clay
+}
+
+# subdom_num : subdomain L for L-scheme
+L = {
+ 1: {'wetting' :Lw,
+ 'nonwetting': Lnw},
+ 2: {'wetting' :Lw,
+ 'nonwetting': Lnw},
+ 3: {'wetting' :Lw,
+ 'nonwetting': Lnw},
+ 4: {'wetting' :Lw,
+ 'nonwetting': Lnw}
+}
+
+# subdom_num : lambda parameter for the L-scheme
+lambda_param = {
+ 1: {'wetting': lambda_w,
+ 'nonwetting': lambda_nw},#
+ 2: {'wetting': lambda_w,
+ 'nonwetting': lambda_nw},#
+ 3: {'wetting': lambda_w,
+ 'nonwetting': lambda_nw},#
+ 4: {'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
+
+
+## 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_perm1w = ft.partial(rel_perm1w)
+_rel_perm1nw = ft.partial(rel_perm1nw)
+_rel_perm2w = ft.partial(rel_perm2w)
+_rel_perm2nw = ft.partial(rel_perm2nw)
+
+subdomain1_rel_perm = {
+ 'wetting': _rel_perm1w,#
+ 'nonwetting': _rel_perm1nw
+}
+
+subdomain2_rel_perm = {
+ 'wetting': _rel_perm2w,#
+ 'nonwetting': _rel_perm2nw
+}
+
+# _rel_perm3 = ft.partial(rel_perm2)
+# subdomain3_rel_perm = subdomain2_rel_perm.copy()
+#
+# _rel_perm4 = ft.partial(rel_perm1)
+# subdomain4_rel_perm = subdomain1_rel_perm.copy()
+
+# dictionary of relative permeabilties on all domains.
+relative_permeability = {
+ 1: subdomain1_rel_perm,
+ 2: subdomain1_rel_perm,
+ 3: subdomain2_rel_perm,
+ 4: 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: subdomain1_rel_perm_prime,
+ 3: subdomain2_rel_perm_prime,
+ 4: subdomain2_rel_perm_prime
+}
+
+
+
+# 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
+# this function needs to be monotonically decreasing in the capillary pressure pc.
+# since in the richards case pc=-pw, this becomes as a function of pw a mono
+# tonically INCREASING function like in our Richards-Richards paper. However
+# since we unify the treatment in the code for Richards and two-phase, we need
+# the same requierment
+# for both cases, two-phase and Richards.
+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=3, 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)
+}
+
+S_pc_sym_prime = {
+ 1: ft.partial(saturation_sym_prime, n_index=3, alpha=0.001),
+ 2: ft.partial(saturation_sym_prime, n_index=3, 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)
+}
+
+sat_pressure_relationship = {
+ 1: ft.partial(saturation, n_index=3, alpha=0.001),
+ 2: ft.partial(saturation, n_index=3, alpha=0.001),
+ 3: ft.partial(saturation, n_index=3, alpha=0.001),
+ 4: 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)
+
+p_e_sym_2patch = {
+ 1: {'wetting': -7 - (1+t*t)*(1 + x*x + y*y),
+ 'nonwetting': -1-t*(1.1 + y + x**2)},
+ 2: {'wetting': -7.0 - (1.0 + t*t)*(1.0 + x*x + y*y),
+ 'nonwetting': -1-t*(1.1 + y + x**2)},
+}
+
+p_e_sym = {
+ 1: {'wetting': p_e_sym_2patch[1]['wetting'],
+ 'nonwetting': p_e_sym_2patch[1]['nonwetting']},
+ 2: {'wetting': p_e_sym_2patch[1]['wetting'],
+ 'nonwetting': p_e_sym_2patch[1]['nonwetting']},
+ 3: {'wetting': p_e_sym_2patch[2]['wetting'],
+ 'nonwetting': p_e_sym_2patch[2]['nonwetting']},
+ 4: {'wetting': p_e_sym_2patch[2]['wetting'],
+ 'nonwetting': p_e_sym_2patch[2]['nonwetting']}
+}
+
+
+# p_e_sym = {
+# 1: {'wetting': 1.0 - (1.0 + t*t)*(10.0 + x*x + (y-5.0)*(y-5.0)),
+# 'nonwetting': - 2 - t*(1 + (y-5.0) + x**2)**2 -sym.sqrt(2+t**2)*(1 + (y-5.0)) },
+# 2: {'wetting': 1.0 - (1.0 + t*t)*(10.0 + x*x + (y-5.0)*(y-5.0)),
+# 'nonwetting': - 2 - t*(1 + (y-5.0) + x**2)**2 -sym.sqrt(2+t**2)*(1 + (y-5.0))},
+# 3: {'wetting': 1.0 - (1.0 + t*t)*(10.0 + x*x + (y-5.0)*(y-5.0)) - (y-5.0)*(y-5.0)*3*sym.sin(-2*t+2*x)*sym.sin(1/2*y-1.2*t),
+# 'nonwetting': - 2 - t*(1 + x**2)**2 -sym.sqrt(2+t**2)},
+# 4: {'wetting': 1.0 - (1.0 + t*t)*(10.0 + x*x + (y-5.0)*(y-5.0)) - (y-5.0)*(y-5.0)*3*sym.sin(-2*t+2*x)*sym.sin(1/2*y-1.2*t),
+# 'nonwetting': - 2 - t*(1 + x**2)**2 -sym.sqrt(2+t**2)}
+# }
+
+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]}
+ )
+
+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)