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Commit d4075f67 authored by Martin Schneider's avatar Martin Schneider
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[doc][model] Formatting variables list

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...@@ -29,9 +29,9 @@ $\begin{equation*} ...@@ -29,9 +29,9 @@ $\begin{equation*}
|B| \frac{S_h(\mathbf{u}^{n+1}_h) - S_h(\mathbf{u}^{n}_h)}{\Delta t} + \sum_{\sigma \in \Sigma_B} F_{B,\sigma}(\mathbf{u}^{n+1}_h) = \int_{B} q \, dx, \quad \forall t_{n+1}\leq T, \; \forall B |B| \frac{S_h(\mathbf{u}^{n+1}_h) - S_h(\mathbf{u}^{n}_h)}{\Delta t} + \sum_{\sigma \in \Sigma_B} F_{B,\sigma}(\mathbf{u}^{n+1}_h) = \int_{B} q \, dx, \quad \forall t_{n+1}\leq T, \; \forall B
\end{equation*}$ \end{equation*}$
* $S_h$: storage term * $S_h:$ storage term
* $F_{B,\sigma}$: flux term over sub control volume face (scvf) * $F_{B,\sigma}:$ 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
- $\Omega$: spatial domain - $\Omega:$ 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__
- $\mathbf{n}$: unit outer normal vector - $\mathbf{n}:$ unit outer normal vector
- $\sigma$: sub control volume face (scvf) - $\sigma:$ 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__
- $\mathbf{n}$: unit outer normal vector - $\mathbf{n}:$ unit outer normal vector
- $\sigma$: sub control volume face (scvf) - $\sigma:$ sub control volume face (scvf)
## Flux term ## Flux term
```cpp ```cpp
......
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