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dumux-course
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4fd6dc56
Commit
4fd6dc56
authored
8 months ago
by
Martin Schneider
Committed by
Timo Koch
8 months ago
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[ex][model][slides] Update slides
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[ex][model][slides] Update slides
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slides/model.md
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4fd6dc56
...
@@ -11,7 +11,7 @@ A DuMu^x^ model is an implementation of a discretized **mathematical model**, ge
...
@@ -11,7 +11,7 @@ A DuMu^x^ model is an implementation of a discretized **mathematical model**, ge
Mathematical model (PDE):
Mathematical model (PDE):
$$
$$
\b
egin{aligned}
\b
egin{aligned}
\f
rac{
\p
artial S(u)}{
\p
artial t} +
\n
abla
\c
dot
\m
athbf{F}(u) = q,
\q
uad
\f
orall (t,
\m
athbf{x})
\i
n (0,T]
\t
imes
\O
mega
\f
rac{
\p
artial S(u)}{
\p
artial t} +
\n
abla
\c
dot
\m
athbf{F}(u) = q
(u)
,
\q
uad
\f
orall (t,
\m
athbf{x})
\i
n (0,T]
\t
imes
\O
mega
\e
nd{aligned}
\e
nd{aligned}
$$
$$
...
@@ -71,12 +71,7 @@ $$
...
@@ -71,12 +71,7 @@ $$
\e
nd{aligned}
\e
nd{aligned}
$$
$$
with
<img
src=
img/box_scv_scvf.png
width=
"80%"
>
-
$c_B^n:$ concentration at time $t_n$ and control volume $B$
-
$c^n_h:$ global discrete solution at time $t_n$, interpolated using __basis functions__
-
$
\m
athbf{n}:$ unit outer normal vector
-
$
\s
igma:$ sub control volume face (scvf)
## Example: Diffusion equation
## Example: Diffusion equation
Discrete model using the Box discretization:
Discrete model using the Box discretization:
...
@@ -87,7 +82,12 @@ $$
...
@@ -87,7 +82,12 @@ $$
\e
nd{aligned}
\e
nd{aligned}
$$
$$
<img
src=
img/box_scv_scvf.png
width=
"80%"
>
with
-
$c_B^n:$ concentration at time $t_n$ and control volume $B$
-
$c^n_h:$ global discrete solution at time $t_n$, interpolated using __basis functions__
-
$
\m
athbf{n}:$ unit outer normal vector
-
$
\s
igma:$ sub control volume face (scvf)
## `LocalResidual`
## `LocalResidual`
The local residual of the diffusion model:
The local residual of the diffusion model:
...
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