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nek5000
giraffe
Commits
0c55420a
Commit
0c55420a
authored
Oct 10, 2016
by
Ron Rahaman
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Added working 2d_transient.i config file
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43daed5d
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examples/heat_conduction/2d_transient_square.i
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0c55420a
#
This
test
solves
a
1
D
transient
heat
equation
#
The
error
is
caclulated
by
comparing
to
the
analytical
solution
#
The
problem
setup
and
analytical
solution
are
taken
from
"Advanced Engineering
# Mathematics, 10th edition"
by
Erwin
Kreyszig
.
#
http
:
//www.amazon.com/AdvancedEngineeringMathematicsErwinKreyszig/dp/0470458364
#
It
is
Example
1
in
section
12.6
on
page
561
[
Mesh
]
type
=
GeneratedMesh
dim
=
2
nx
=
40
ny
=
40
xmax
=
80
ymax
=
80
[]
[
Variables
]
[
.
/
T
]
[
..
/
]
[]
[
ICs
]
[
.
/
T_IC
]
type
=
FunctionIC
variable
=
T
function
=
'
100
*
sin
(
3.14159
*
x
/
80
)
*
sin
(
3.14159
*
y
/
80
)
'
[
..
/
]
[]
[
Kernels
]
[
.
/
HeatDiff
]
type
=
HeatConduction
variable
=
T
[
..
/
]
[
.
/
HeatTdot
]
type
=
HeatConductionTimeDerivative
variable
=
T
[
..
/
]
[]
[
BCs
]
[
.
/
left
]
type
=
DirichletBC
variable
=
T
boundary
=
left
value
=
0
[
..
/
]
[
.
/
right
]
type
=
DirichletBC
variable
=
T
boundary
=
right
value
=
0
[
..
/
]
[
.
/
top
]
type
=
DirichletBC
variable
=
T
boundary
=
top
value
=
0
[
..
/
]
[
.
/
bottom
]
type
=
DirichletBC
variable
=
T
boundary
=
bottom
value
=
0
[
..
/
]
[]
[
Materials
]
[
.
/
k
]
type
=
GenericConstantMaterial
prop_names
=
'
thermal_conductivity
'
prop_values
=
'
0.95
'
#
copper
in
cal
/
(
cm
sec
C
)
block
=
0
[
..
/
]
[
.
/
cp
]
type
=
GenericConstantMaterial
prop_names
=
'
specific_heat
'
prop_values
=
'
0.092
'
#
copper
in
cal
/
(
g
C
)
block
=
0
[
..
/
]
[
.
/
rho
]
type
=
GenericConstantMaterial
prop_names
=
'
density
'
prop_values
=
'
8.92
'
#
copper
in
g
/
(
cm
^
3
)
block
=
0
[
..
/
]
[]
[
Postprocessors
]
[
.
/
error
]
type
=
NodalL2Error
function
=
'
100
*
sin
(
3.14159
*
x
/
80
)
*
exp
(

0.95
/
(
0.092
*
8.92
)
*
3.14159
^
2
/
80
^
2
*
t
)
'
#
T
(
x
,
t
)
=
100
sin
(
pix
/
L
)
exp
(

rho
/
(
cp
k
)
pi
^
2
/
L
^
2
t
)
variable
=
T
[
..
/
]
[]
[
Executioner
]
type
=
Transient
scheme
=
bdf2
nl_rel_tol
=
1e12
l_tol
=
1e6
dt
=
2
end_time
=
100
petsc_options_iname
=
'

pc_type

pc_hypre_type
'
petsc_options_value
=
'
hypre
boomeramg
'
[]
[
Outputs
]
exodus
=
true
print_perf_log
=
true
[]
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