diff --git a/slides/model.md b/slides/model.md index 0cdab3ac63c500ffb74c8ec36b0e3a857aee1caa..fc9fb5ad74fddbefbef991d76b9291b33993c782 100644 --- a/slides/model.md +++ b/slides/model.md @@ -1,13 +1,13 @@ --- -title: Implementing a Model in DuMuX +title: Implementing a Model in DuMu^x^ --- -# What is a DuMu<sup>X</sup> model +# What is a DuMu^x^ model -## What is a DuMu<sup>X</sup> model -A DuMu<sup>X</sup> model is an implementation of a discretized **mathematical model**, generally given by partial differential equations. +## What is a DuMu^x^ model +A DuMu^x^ model is an implementation of a discretized **mathematical model**, generally given by partial differential equations. -## What is a DuMu<sup>X</sup> model +## What is a DuMu^x^ model Mathematical model (PDE): $\begin{equation*} \small @@ -22,7 +22,7 @@ $\begin{equation*} |B| \frac{S_h(\mathbf{u}^{n+1}_h) - S_h(\mathbf{u}^{n}_h)}{\Delta t} + \sum_{\sigma \in \Sigma_B} F_{B,\sigma}(\mathbf{u}^{n+1}_h) = \int_{B} q^{n+1} \, dx, \quad \forall t_{n+1}\leq T, \; \forall B \end{equation*}$ -## What is a DuMu<sup>X</sup> model +## What is a DuMu^x^ model Discrete model, e.g. using finite volumes: $\begin{equation*} \small @@ -33,7 +33,7 @@ $\begin{equation*} * $F_{B,\sigma}:$ flux term over sub control volume face (scvf) * $q:$ source term -Where to implement these terms in DuMu<sup>X</sup>? +Where to implement these terms in DuMu^x^? `LocalResidual`