Commit aeacd3d6 authored by Melanie Lipp's avatar Melanie Lipp Committed by Martin Schneider

Mention where 'actual equations' can be found.

parent f8021fa7
\section{Models}
Here the basic definitions, the general models concept, and a list of
models available in \Dumux are given.
models available in \Dumux are given. The actual differential equations
can be found in the localresiduals (see doxygen documentation of the
model's \texttt{LocalResidual} class).
\subsection{Basic Definitions and Assumptions}
The basic definitions and assumptions are made, using the example
......@@ -134,7 +136,7 @@ Dalton's law assumes that the gases in the mixture are non-interacting (with eac
p = \sum_{i}^{}p_i.
\end{equation}
Here $p_i$ refers to the partial pressure of component i.
As an example, if two equal volumes of gas A and gas B are mixed, the volume of the mixture stays the same but the pressures add up (see Figure \ref{fig:dalton1}).
As an example, if two equal volumes of gas A and gas B are mixed, the volume of the mixture stays the same but the pressures add up (see Figure \ref{fig:dalton1}).
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\begin{figure}[ht]
\centering
......@@ -154,7 +156,7 @@ or for an arbitrary number of gases:
\end{equation}
%
\subsubsection{Amagat's law}
Amagat's law assumes that the volumes of the component gases are additive; the interactions of the different gases are the same as the average interactions of the components. This is known as Amagat's law:
Amagat's law assumes that the volumes of the component gases are additive; the interactions of the different gases are the same as the average interactions of the components. This is known as Amagat's law:
%
\begin{equation}
V = \sum_{i}^{}V_i.
......@@ -171,7 +173,7 @@ As an example, if two volumes of gas A and B at equal pressure are mixed, the pr
%
The density of the mixture, $\varrho$, can be calculated as follows:
\begin{equation}
\varrho = \frac{m}{V} = \frac{m}{V_\mathrm{A} + V_\mathrm{B}} = \frac{m}{\frac{m_\mathrm{A}}{\varrho_\mathrm{A}} \frac{m_\mathrm{B}}{\varrho_\mathrm{B}}} =
\varrho = \frac{m}{V} = \frac{m}{V_\mathrm{A} + V_\mathrm{B}} = \frac{m}{\frac{m_\mathrm{A}}{\varrho_\mathrm{A}} \frac{m_\mathrm{B}}{\varrho_\mathrm{B}}} =
\frac{m}{\frac{X_\mathrm{A} m}{\varrho_\mathrm{A}} \frac{X_\mathrm{B} m}{\varrho_\mathrm{B}}} = \frac{1}{\frac{X_\mathrm{A}}{\varrho_\mathrm{A}} \frac{X_\mathrm{B}}{\varrho_\mathrm{B}}},
\end{equation}
%
......@@ -182,7 +184,7 @@ or for an arbitrary number of gases:
\end{equation}
%
\subsubsection{Ideal gases}
An ideal gas is defined as a gas whose molecules are spaced so far apart that the behavior of a molecule is not influenced by the presence of other molecules.
An ideal gas is defined as a gas whose molecules are spaced so far apart that the behavior of a molecule is not influenced by the presence of other molecules.
This assumption is usually valid at low pressures and high temperatures. The ideal gas law states that, for one gas:
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\begin{equation}
......@@ -193,7 +195,7 @@ Using the assumption of ideal gases and either Dalton's law or Amagat's law lead
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\begin{equation}
\varrho = \frac{p}{RT} \sum_{i}^{}M_i x_i ; \quad \varrho_m = \frac{p}{RT}.
\end{equation}
\end{equation}
%
\subsection{Available Models}
A list of all available models can be found
......@@ -203,7 +205,7 @@ The documentation includes a detailed description for every model.
\subsubsection{Time discretization}
Our systems of partial differential equations are discretized in space and in time.
Our systems of partial differential equations are discretized in space and in time.
Let us consider the general case of a balance equation of the following form
\begin{equation}\label{eq:generalbalance}
......
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