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David Seus
LDD-for-two-phase-flow-systems
Commits
d86f1eaa
Commit
d86f1eaa
authored
Aug 16, 2019
by
David Seus
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fix weird git fuckug
parent
60d6185f
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TP-TP-2-patch-constant-solution/TP-TP-2-patch-constant-solution.py
+61
-224
61 additions, 224 deletions
...atch-constant-solution/TP-TP-2-patch-constant-solution.py
with
61 additions
and
224 deletions
TP-TP-2-patch-constant-solution/TP-TP-2-patch-constant-solution.py
+
61
−
224
View file @
d86f1eaa
...
@@ -7,11 +7,32 @@ import typing as tp
...
@@ -7,11 +7,32 @@ import typing as tp
import
domainPatch
as
dp
import
domainPatch
as
dp
import
LDDsimulation
as
ldd
import
LDDsimulation
as
ldd
import
functools
as
ft
import
functools
as
ft
import
helpers
as
hlp
#import ufl as ufl
#import ufl as ufl
# init sympy session
# init sympy session
sym
.
init_printing
()
sym
.
init_printing
()
solver_tol
=
5E-6
############ GRID #######################ü
mesh_resolution
=
20
timestep_size
=
0.01
number_of_timesteps
=
100
# 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
=
10
starttime
=
0
Lw
=
1
/
timestep_size
Lnw
=
Lw
l_param_w
=
40
l_param_nw
=
40
include_gravity
=
True
##### Domain and Interface ####
##### Domain and Interface ####
# global simulation domain domain
# global simulation domain domain
sub_domain0_vertices
=
[
df
.
Point
(
-
1.0
,
-
1.0
),
#
sub_domain0_vertices
=
[
df
.
Point
(
-
1.0
,
-
1.0
),
#
...
@@ -80,15 +101,6 @@ isRichards = {
...
@@ -80,15 +101,6 @@ isRichards = {
}
}
############ GRID #######################ü
mesh_resolution
=
41
timestep_size
=
0.01
number_of_timesteps
=
100
# 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
=
{
#
viscosity
=
{
#
# subdom_num : viscosity
# subdom_num : viscosity
1
:
{
'
wetting
'
:
1
,
1
:
{
'
wetting
'
:
1
,
...
@@ -116,19 +128,19 @@ porosity = {#
...
@@ -116,19 +128,19 @@ porosity = {#
L
=
{
#
L
=
{
#
# subdom_num : subdomain L for L-scheme
# subdom_num : subdomain L for L-scheme
1
:
{
'
wetting
'
:
0.25
,
1
:
{
'
wetting
'
:
Lw
,
'
nonwetting
'
:
0.25
},
#
'
nonwetting
'
:
Lnw
},
#
2
:
{
'
wetting
'
:
0.25
,
2
:
{
'
wetting
'
:
Lw
,
'
nonwetting
'
:
0.25
}
'
nonwetting
'
:
Lnw
}
}
}
l_param
=
40
lambda_param
=
{
#
lambda_param
=
{
#
# subdom_num : lambda parameter for the L-scheme
# subdom_num : lambda parameter for the L-scheme
1
:
{
'
wetting
'
:
l_param
,
1
:
{
'
wetting
'
:
l_param
_w
,
'
nonwetting
'
:
l_param
},
#
'
nonwetting
'
:
l_param
_nw
},
#
2
:
{
'
wetting
'
:
l_param
,
2
:
{
'
wetting
'
:
l_param
_w
,
'
nonwetting
'
:
l_param
}
'
nonwetting
'
:
l_param
_nw
}
}
}
## relative permeabilty functions on subdomain 1
## relative permeabilty functions on subdomain 1
...
@@ -177,7 +189,7 @@ def rel_perm1w_prime(s):
...
@@ -177,7 +189,7 @@ def rel_perm1w_prime(s):
def
rel_perm1nw_prime
(
s
):
def
rel_perm1nw_prime
(
s
):
# relative permeabilty on subdomain1
# relative permeabilty on subdomain1
return
2
*
(
1
-
s
)
return
-
2
*
(
1
-
s
)
# # definition of the derivatives of the relative permeabilities
# # definition of the derivatives of the relative permeabilities
# # relative permeabilty functions on subdomain 1
# # relative permeabilty functions on subdomain 1
...
@@ -187,7 +199,7 @@ def rel_perm1nw_prime(s):
...
@@ -187,7 +199,7 @@ def rel_perm1nw_prime(s):
#
#
# def rel_perm2nw_prime(s):
# def rel_perm2nw_prime(s):
# # relative permeabilty on subdomain1
# # relative permeabilty on subdomain1
# return 2*(l_param_w1-s)
# return
-
2*(l_param_w1-s)
_rel_perm1w_prime
=
ft
.
partial
(
rel_perm1w_prime
)
_rel_perm1w_prime
=
ft
.
partial
(
rel_perm1w_prime
)
_rel_perm1nw_prime
=
ft
.
partial
(
rel_perm1nw_prime
)
_rel_perm1nw_prime
=
ft
.
partial
(
rel_perm1nw_prime
)
...
@@ -364,211 +376,36 @@ p_e_sym = {
...
@@ -364,211 +376,36 @@ p_e_sym = {
# 5: {'wetting': 1.0 - (1.0 + t*t)*(1.0 + x*x + y*y)}
# 5: {'wetting': 1.0 - (1.0 + t*t)*(1.0 + x*x + y*y)}
}
}
# pc_e_sym = {
pc_e_sym
=
dict
()
# 1: -1*p_e_sym[1]['wetting'],
# 2: -1*p_e_sym[2]['wetting'],
# # 3: -1*p_e_sym[3]['wetting'],
# # 4: -1*p_e_sym[4]['wetting'],
# # 5: -1*p_e_sym[5]['wetting']
# }
pc_e_sym
=
{
1
:
p_e_sym
[
1
][
'
nonwetting
'
]
-
p_e_sym
[
1
][
'
wetting
'
],
2
:
p_e_sym
[
2
][
'
nonwetting
'
]
-
p_e_sym
[
2
][
'
wetting
'
],
# 3: -1*p_e_sym[3]['wetting'],
# 4: -1*p_e_sym[4]['wetting'],
# 5: -1*p_e_sym[5]['wetting']
}
# #### 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(sym.Piecewise((S_pc_rel[1](p1_nw - p1_w), (p1_nw - p1_w) > 0), (1, True) ), t, 1)
# dtS1_nw = -porosity[1]*sym.diff(sym.Piecewise((S_pc_rel[1](p1_nw - p1_w), (p1_nw - p1_w) > 0), (1, True) ), 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'](sym.Piecewise((S_pc_rel[1](p1_nw - p1_w), (p1_nw - p1_w) > 0), (1, True) ))*sym.diff(p1_w, x, 1), x, 1)
# dydyflux1_w = -1/viscosity[1]['wetting']*sym.diff(relative_permeability[1]['wetting'](sym.Piecewise((S_pc_rel[1](p1_nw - p1_w), (p1_nw - p1_w) > 0), (1, True) ))*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-sym.Piecewise((S_pc_rel[1](p1_nw - p1_w), (p1_nw - p1_w) > 0), (1, True) ))*sym.diff(p1_nw, x, 1), x, 1)
# dydyflux1_nw = -1/viscosity[1]['nonwetting']*sym.diff(relative_permeability[1]['nonwetting'](1-sym.Piecewise((S_pc_rel[1](p1_nw - p1_w), (p1_nw - p1_w) > 0), (1, True) ))*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(sym.Piecewise((sym.Piecewise((S_pc_rel[2](p2_nw - p2_w), (p2_nw - p2_w) > 0), (1, True) ), (p2_nw - p2_w) > 0), (1, True) ), t, 1)
# dtS2_nw = -porosity[2]*sym.diff(sym.Piecewise((S_pc_rel[2](p2_nw - p2_w), (p2_nw - p2_w) > 0), (1, True) ), 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'](sym.Piecewise((S_pc_rel[2](p2_nw - p2_w), (p2_nw - p2_w) > 0), (1, True) ))*sym.diff(p2_w, x, 1), x, 1)
# dydyflux2_w = -1/viscosity[2]['wetting']*sym.diff(relative_permeability[2]['wetting'](sym.Piecewise((S_pc_rel[2](p2_nw - p2_w), (p2_nw - p2_w) > 0), (1, True) ))*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-sym.Piecewise((S_pc_rel[2](p2_nw - p2_w), (p2_nw - p2_w) > 0), (1, True) ))*sym.diff(p2_nw, x, 1), x, 1)
# dydyflux2_nw = -1/viscosity[2]['nonwetting']*sym.diff(relative_permeability[2]['nonwetting'](1-sym.Piecewise((S_pc_rel[2](p2_nw - p2_w), (p2_nw - p2_w) > 0), (1, True) ))*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)}}
# }
# turn above symbolic code into exact solution for dolphin and
# construct the rhs that matches the above exact solution.
dtS
=
dict
()
div_flux
=
dict
()
source_expression
=
dict
()
exact_solution
=
dict
()
initial_condition
=
dict
()
for
subdomain
,
isR
in
isRichards
.
items
():
for
subdomain
,
isR
in
isRichards
.
items
():
dtS
.
update
({
subdomain
:
dict
()})
div_flux
.
update
({
subdomain
:
dict
()})
source_expression
.
update
({
subdomain
:
dict
()})
exact_solution
.
update
({
subdomain
:
dict
()})
initial_condition
.
update
({
subdomain
:
dict
()})
if
isR
:
if
isR
:
subdomain_has_phases
=
[
"
wetting
"
]
pc_e_sym
.
update
({
subdomain
:
-
p_e_sym
[
subdomain
][
'
wetting
'
]})
else
:
else
:
subdomain_has_phases
=
[
"
wetting
"
,
"
nonwetting
"
]
pc_e_sym
.
update
({
subdomain
:
p_e_sym
[
subdomain
][
'
nonwetting
'
]
-
p_e_sym
[
subdomain
][
'
wetting
'
]})
# conditional for S_pc_prime
symbols
=
{
"
x
"
:
x
,
pc
=
pc_e_sym
[
subdomain
]
"
y
"
:
y
,
dtpc
=
sym
.
diff
(
pc
,
t
,
1
)
"
t
"
:
t
}
dxpc
=
sym
.
diff
(
pc
,
x
,
1
)
# turn above symbolic code into exact solution for dolphin and
dypc
=
sym
.
diff
(
pc
,
y
,
1
)
# construct the rhs that matches the above exact solution.
S
=
sym
.
Piecewise
((
S_pc_sym
[
subdomain
](
pc
),
pc
>
0
),
(
1
,
True
))
exact_solution_example
=
hlp
.
generate_exact_solution_expressions
(
dS
=
sym
.
Piecewise
((
S_pc_sym_prime
[
subdomain
](
pc
),
pc
>
0
),
(
0
,
True
))
symbols
=
symbols
,
for
phase
in
subdomain_has_phases
:
isRichards
=
isRichards
,
# Turn above symbolic expression for exact solution into c code
symbolic_pressure
=
p_e_sym
,
exact_solution
[
subdomain
].
update
(
symbolic_capillary_pressure
=
pc_e_sym
,
{
phase
:
sym
.
printing
.
ccode
(
p_e_sym
[
subdomain
][
phase
])}
saturation_pressure_relationship
=
S_pc_sym
,
)
saturation_pressure_relationship_prime
=
S_pc_sym_prime
,
# save the c code for initial conditions
viscosity
=
viscosity
,
initial_condition
[
subdomain
].
update
(
porosity
=
porosity
,
{
phase
:
sym
.
printing
.
ccode
(
p_e_sym
[
subdomain
][
phase
].
subs
(
t
,
0
))}
relative_permeability
=
relative_permeability
,
)
relative_permeability_prime
=
ka_prime
,
if
phase
==
"
nonwetting
"
:
densities
=
densities
,
dtS
[
subdomain
].
update
(
gravity_acceleration
=
gravity_acceleration
,
{
phase
:
-
porosity
[
subdomain
]
*
dS
*
dtpc
}
include_gravity
=
include_gravity
,
)
else
:
dtS
[
subdomain
].
update
(
{
phase
:
porosity
[
subdomain
]
*
dS
*
dtpc
}
)
pa
=
p_e_sym
[
subdomain
][
phase
]
dxpa
=
sym
.
diff
(
pa
,
x
,
1
)
dxdxpa
=
sym
.
diff
(
pa
,
x
,
2
)
dypa
=
sym
.
diff
(
pa
,
y
,
1
)
dydypa
=
sym
.
diff
(
pa
,
y
,
2
)
mu
=
viscosity
[
subdomain
][
phase
]
ka
=
relative_permeability
[
subdomain
][
phase
]
dka
=
ka_prime
[
subdomain
][
phase
]
rho
=
densities
[
subdomain
][
phase
]
g
=
gravity_acceleration
if
phase
==
"
nonwetting
"
:
# x part of div(flux) for nonwetting
dxdxflux
=
-
1
/
mu
*
dka
(
1
-
S
)
*
dS
*
dxpc
*
dxpa
+
1
/
mu
*
dxdxpa
*
ka
(
1
-
S
)
# y part of div(flux) for nonwetting
dydyflux
=
-
1
/
mu
*
dka
(
1
-
S
)
*
dS
*
dypc
*
(
dypa
-
rho
*
g
)
\
+
1
/
mu
*
dydypa
*
ka
(
1
-
S
)
else
:
# x part of div(flux) for wetting
dxdxflux
=
1
/
mu
*
dka
(
S
)
*
dS
*
dxpc
*
dxpa
+
1
/
mu
*
dxdxpa
*
ka
(
S
)
# y part of div(flux) for wetting
dydyflux
=
1
/
mu
*
dka
(
S
)
*
dS
*
dypc
*
(
dypa
-
rho
*
g
)
+
1
/
mu
*
dydypa
*
ka
(
S
)
div_flux
[
subdomain
].
update
({
phase
:
dxdxflux
+
dydyflux
})
contructed_rhs
=
dtS
[
subdomain
][
phase
]
-
div_flux
[
subdomain
][
phase
]
source_expression
[
subdomain
].
update
(
{
phase
:
sym
.
printing
.
ccode
(
contructed_rhs
)}
)
)
# print(f"source_expression[{subdomain}][{phase}] =", source_expression[subdomain][phase])
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.
# Dictionary of dirichlet boundary conditions.
dirichletBC
=
dict
()
dirichletBC
=
dict
()
...
@@ -612,7 +449,7 @@ write_to_file = {
...
@@ -612,7 +449,7 @@ write_to_file = {
# initialise LDD simulation class
# initialise LDD simulation class
simulation
=
ldd
.
LDDsimulation
(
tol
=
1E-14
,
LDDsolver_tol
=
1E-6
,
debug
=
Fals
e
)
simulation
=
ldd
.
LDDsimulation
(
tol
=
1E-14
,
LDDsolver_tol
=
solver_tol
,
debug
=
Tru
e
)
simulation
.
set_parameters
(
output_dir
=
"
./output/
"
,
#
simulation
.
set_parameters
(
output_dir
=
"
./output/
"
,
#
subdomain_def_points
=
subdomain_def_points
,
#
subdomain_def_points
=
subdomain_def_points
,
#
isRichards
=
isRichards
,
#
isRichards
=
isRichards
,
#
...
@@ -635,7 +472,7 @@ simulation.set_parameters(output_dir = "./output/",#
...
@@ -635,7 +472,7 @@ simulation.set_parameters(output_dir = "./output/",#
dirichletBC_expression_strings
=
dirichletBC
,
#
dirichletBC_expression_strings
=
dirichletBC
,
#
exact_solution
=
exact_solution
,
#
exact_solution
=
exact_solution
,
#
densities
=
densities
,
densities
=
densities
,
include_gravity
=
True
,
include_gravity
=
include_gravity
,
write2file
=
write_to_file
,
#
write2file
=
write_to_file
,
#
)
)
...
...
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