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dumux-course
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d4075f67
Commit
d4075f67
authored
1 year ago
by
Martin Schneider
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[doc][model] Formatting variables list
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a1288d3f
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!176
Feature/update new model slides
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#30487
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d4075f67
...
@@ -29,9 +29,9 @@ $\begin{equation*}
...
@@ -29,9 +29,9 @@ $\begin{equation*}
|B|
\f
rac{S_h(
\m
athbf{u}^{n+1}_h) - S_h(
\m
athbf{u}^{n}_h)}{
\D
elta t} +
\s
um_{
\s
igma
\i
n
\S
igma_B} F_{B,
\s
igma}(
\m
athbf{u}^{n+1}_h) =
\i
nt_{B} q
\,
dx,
\q
uad
\f
orall t_{n+1}
\l
eq T,
\;
\f
orall B
|B|
\f
rac{S_h(
\m
athbf{u}^{n+1}_h) - S_h(
\m
athbf{u}^{n}_h)}{
\D
elta t} +
\s
um_{
\s
igma
\i
n
\S
igma_B} F_{B,
\s
igma}(
\m
athbf{u}^{n+1}_h) =
\i
nt_{B} q
\,
dx,
\q
uad
\f
orall t_{n+1}
\l
eq T,
\;
\f
orall B
\e
nd{equation
*
}$
\e
nd{equation
*
}$
*
$S_h
$
: storage term
*
$S_h:
$
storage term
*
$F_{B,
\s
igma}
$
: flux term over sub control volume face (scvf)
*
$F_{B,
\s
igma}:
$
flux term over sub control volume face (scvf)
*
$q$ source term
*
$q
:
$ source term
Where to implement these terms in DuMu
<sup>
X
</sup>
?
Where to implement these terms in DuMu
<sup>
X
</sup>
?
...
@@ -57,10 +57,10 @@ $\begin{equation}
...
@@ -57,10 +57,10 @@ $\begin{equation}
with
with
-
$c
$
: concentration
-
$c:
$
concentration
-
$D
$
: constant diffusion coefficient
-
$D:
$
constant diffusion coefficient
-
$
\O
mega
$
: spatial domain
-
$
\O
mega:
$
spatial domain
-
$T
$
: end time
-
$T:
$
end time
## Example: Diffusion equation
## Example: Diffusion equation
Discrete model using the Box discretization:
Discrete model using the Box discretization:
...
@@ -71,10 +71,10 @@ $\begin{equation}
...
@@ -71,10 +71,10 @@ $\begin{equation}
with
with
-
$c_B^n
$
: concentration at time $t_n$ and control volume $B$
-
$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__
-
$c^n_h:
$
global discrete solution at time $t_n$, interpolated using __basis functions__
-
$
\m
athbf{n}
$
: unit outer normal vector
-
$
\m
athbf{n}:
$
unit outer normal vector
-
$
\s
igma
$
: sub control volume face (scvf)
-
$
\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:
...
@@ -118,9 +118,9 @@ F_{B,\sigma} = -D \nabla c_h^{n+1} \cdot \boldsymbol{n}_{B,\sigma} \vert \sigma
...
@@ -118,9 +118,9 @@ F_{B,\sigma} = -D \nabla c_h^{n+1} \cdot \boldsymbol{n}_{B,\sigma} \vert \sigma
with
with
-
$c^n_h
$
: global discrete solution at time $t_n$, interpolated using __basis functions__
-
$c^n_h:
$
global discrete solution at time $t_n$, interpolated using __basis functions__
-
$
\m
athbf{n}
$
: unit outer normal vector
-
$
\m
athbf{n}:
$
unit outer normal vector
-
$
\s
igma
$
: sub control volume face (scvf)
-
$
\s
igma:
$
sub control volume face (scvf)
## Flux term
## Flux term
```
cpp
```
cpp
...
...
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