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Commit 0b9933b0 authored by David's avatar David
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add TPR layered soil example

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Two-phase-Richards/multi-patch/layered_soil/TP-R-layered_soil.py 0 → 100755
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#!/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-R-layered-soil-all-params-set-one"
max_iter_num = 1000
FEM_Lagrange_degree = 1
mesh_study = False
resolutions = {
# 1: 1e-7, # h=2
# 2: 2e-5, # h=1.1180
# 4: 1e-6, # h=0.5590
# 8: 1e-6, # h=0.2814
16: 1e-6, # h=0.1412
# 32: 1e-6,
# 64: 5e-7,
# 128: 5e-7
}
############ GRID #######################
# mesh_resolution = 20
timestep_size = 0.001
number_of_timesteps = 40
plot_timestep_every = 1
# 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]
Lw = 0.025 #/timestep_size
Lnw=Lw
lambda_w = 40
lambda_nw = 40
include_gravity = True
debugflag = False
analyse_condition = False
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
}
# 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: True,
2: True,
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 = 1
# 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},#
}
intrinsic_permeability = {
1: 1,
2: 1,
3: 1,
4: 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
## 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_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 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 subdomain1
return intrinsic_permeability[2]*3*s**2
def rel_perm2nw_prime(s):
# relative permeabilty on subdomain1
return -1*intrinsic_permeability[2]*3*(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: 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=6, alpha=0.001),
4: ft.partial(saturation_sym, n_index=6, 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=6, alpha=0.001),
4: ft.partial(saturation_sym_prime, n_index=6, 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=6, alpha=0.001),
4: ft.partial(saturation, n_index=6, 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': 0.0*t}, #-1-t*(1.1 + y + x**2)**2},
2: {'wetting': -7.0 - (1.0 + t*t)*(1.0 + x*x),
'nonwetting': (-1-t*(1.1 + x**2)**2 - sym.sqrt(5+t**2))*y**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]}
)
# read this file and print it to std out. This way the simulation can produce a
# log file with ./TP-R-layered_soil.py | tee simulation.log
f = open('TP-R-layered_soil.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)
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