From d4075f678dfc3005c9f596cd02545040c8256ef5 Mon Sep 17 00:00:00 2001 From: Martin Schneider <martin.schneider@iws.uni-stuttgart.de> Date: Sun, 2 Apr 2023 13:14:50 +0200 Subject: [PATCH] [doc][model] Formatting variables list --- slides/model.md | 28 ++++++++++++++-------------- 1 file changed, 14 insertions(+), 14 deletions(-) diff --git a/slides/model.md b/slides/model.md index 2123761c..76bef5a1 100644 --- a/slides/model.md +++ b/slides/model.md @@ -29,9 +29,9 @@ $\begin{equation*} |B| \frac{S_h(\mathbf{u}^{n+1}_h) - S_h(\mathbf{u}^{n}_h)}{\Delta t} + \sum_{\sigma \in \Sigma_B} F_{B,\sigma}(\mathbf{u}^{n+1}_h) = \int_{B} q \, dx, \quad \forall t_{n+1}\leq T, \; \forall B \end{equation*}$ -* $S_h$: storage term -* $F_{B,\sigma}$: flux term over sub control volume face (scvf) -* $q$ source term +* $S_h:$ storage term +* $F_{B,\sigma}:$ flux term over sub control volume face (scvf) +* $q:$ source term Where to implement these terms in DuMu<sup>X</sup>? @@ -57,10 +57,10 @@ $\begin{equation} with -- $c$: concentration -- $D$: constant diffusion coefficient -- $\Omega$: spatial domain -- $T$: end time +- $c:$ concentration +- $D:$ constant diffusion coefficient +- $\Omega:$ spatial domain +- $T:$ end time ## Example: Diffusion equation Discrete model using the Box discretization: @@ -71,10 +71,10 @@ $\begin{equation} 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__ -- $\mathbf{n}$: unit outer normal vector -- $\sigma$: sub control volume face (scvf) +- $c_B^n:$ concentration at time $t_n$ and control volume $B$ +- $c^n_h:$ global discrete solution at time $t_n$, interpolated using __basis functions__ +- $\mathbf{n}:$ unit outer normal vector +- $\sigma:$ sub control volume face (scvf) ## Example: Diffusion equation 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 with -- $c^n_h$: global discrete solution at time $t_n$, interpolated using __basis functions__ -- $\mathbf{n}$: unit outer normal vector -- $\sigma$: sub control volume face (scvf) +- $c^n_h:$ global discrete solution at time $t_n$, interpolated using __basis functions__ +- $\mathbf{n}:$ unit outer normal vector +- $\sigma:$ sub control volume face (scvf) ## Flux term ```cpp -- GitLab