From eaedbfb8a8c3fb056565eb4ee18ebe8671909466 Mon Sep 17 00:00:00 2001
From: Thomas Fetzer <thomas.fetzer@iws.uni-stuttgart.de>
Date: Thu, 7 Mar 2013 17:18:19 +0000
Subject: [PATCH] [ handbook ] changed BOX to box, added cc-method, corrected
references, made grad bold
git-svn-id: svn://svn.iws.uni-stuttgart.de/DUMUX/dumux/trunk@10343 2fb0f335-1f38-0410-981e-8018bf24f1b0
---
doc/handbook/NewtonInANutshell.tex | 2 +-
doc/handbook/dumux-handbook.tex | 2 +-
doc/handbook/spatialdiscretization.tex | 14 +++++++-------
doc/handbook/structure.tex | 4 +++-
doc/handbook/tutorial.tex | 2 +-
5 files changed, 13 insertions(+), 11 deletions(-)
diff --git a/doc/handbook/NewtonInANutshell.tex b/doc/handbook/NewtonInANutshell.tex
index d6425d56a8..a64ab420f9 100644
--- a/doc/handbook/NewtonInANutshell.tex
+++ b/doc/handbook/NewtonInANutshell.tex
@@ -7,7 +7,7 @@ Coming back to the example of chapter \ref{flow} the following mass conservation
\phi \frac{\partial \varrho_\alpha S_\alpha}{\partial t}
-
\text{div} \left\{
- \varrho_\alpha \frac{k_{r\alpha}}{\mu_\alpha} \mbox{\bf K} \left(\text{grad}\, p_\alpha - \varrho_{\alpha} \mbox{\bf g} \right)
+ \varrho_\alpha \frac{k_{r\alpha}}{\mu_\alpha} \mbox{\bf K} \left(\grad\, p_\alpha - \varrho_{\alpha} \mbox{\bf g} \right)
\right\} - q_\alpha} _
{\textbf{f}(\textbf{u}^r)}
= 0 \; .
diff --git a/doc/handbook/dumux-handbook.tex b/doc/handbook/dumux-handbook.tex
index ce5d466353..c900e5d29b 100644
--- a/doc/handbook/dumux-handbook.tex
+++ b/doc/handbook/dumux-handbook.tex
@@ -127,7 +127,7 @@
\newtheorem{warn}[exc]{Warning}
\newtheorem{justCounting}{}
-\DeclareMathOperator{\grad}{grad}
+\DeclareMathOperator{\grad}{\bf grad}
\DeclareMathOperator{\curl}{curl}
\DeclareMathOperator{\Div}{div}
diff --git a/doc/handbook/spatialdiscretization.tex b/doc/handbook/spatialdiscretization.tex
index 61913dde10..e6cec09773 100644
--- a/doc/handbook/spatialdiscretization.tex
+++ b/doc/handbook/spatialdiscretization.tex
@@ -1,17 +1,17 @@
\section{Implicit Spatial Discretization Schemes}\label{spatialdiscretization}
-For the implicit models there are two spatial discretization schemes (BOX and Cell Centered Finite Volume Method) available which are shortly introduced
+For the implicit models there are two spatial discretization schemes (box and Cell Centered Finite Volume Method) available which are shortly introduced
in this section.
\subsection{Box method - A short introduction}\label{box}
-The so called BOX-method is unites the advantages of the finite-volume (FV) and finite-element (FE) methods.
+The so called box method unites the advantages of the finite-volume (FV) and finite-element (FE) methods.
First, the model domain $G$ is discretized with a FE mesh consisting of nodes i and corresponding elements $E_k$. Then, a secondary FV mesh is constructed by connecting the midpoints and barycenters of the elements surrounding node i creating a box $B_i$ around node i (see Figure \ref{pc:box}a).
\begin{figure} [h]
\includegraphics[width=0.8\linewidth,keepaspectratio]{EPS/box_disc}
-\caption{\label{pc:box} Discretization of the BOX-method}
+\caption{\label{pc:box} Discretization of the box method}
\end{figure}
The FE mesh divides the box $B_i$ into subcontrolvolumes (scv's) $b^k_i$ (see Figure \ref{pc:box}b). Figure \ref{pc:box}c shows the finite element $E_k$ and the scv's $b^k_i$ inside $E_k$, which belong to four different boxes $B_i$. Also necessary for the discretization are the faces of the subcontrolvolumes (scvf's) $e^k_{ij}$ between the scv's $b^k_i$ and $b^k_j$, where $|e^k_{ij}|$ is the length of the scvf. The integration points $x^k_{ij}$ on $e^k_{ij}$ and the outer normal vector $\mathbf n^k_{ij}$ are also to be defined (see Figure \ref{pc:box}c).
@@ -33,7 +33,7 @@ In the following, the discretization of the balance equation is going to be deri
\end{equation}
where term 1 describes the changes of entity $u$ within a control volume over time, term 2 the advective, diffusive and dispersive fluxes over the interfaces of the control volume and term 3 is the source and sink term. $G$ denotes the model domain and $F(u) = F(\mathbf v, p) = F(\mathbf v(x,t), p(x,t))$.
-Like the FE method, the BOX-method follows the principle of weighted residuals. In the function $f(u)$ the unknown $u$ is approximated by discrete values at the nodes of the FE mesh $\hat u_i$ and linear basis functions $N_i$ yielding an approximate function $f(\tilde u)$. For $u\in \lbrace \mathbf v, p, x^\kappa \rbrace$ this means
+Like the FE method, the box method follows the principle of weighted residuals. In the function $f(u)$ the unknown $u$ is approximated by discrete values at the nodes of the FE mesh $\hat u_i$ and linear basis functions $N_i$ yielding an approximate function $f(\tilde u)$. For $u\in \lbrace \mathbf v, p, x^\kappa \rbrace$ this means
\begin{minipage}[b]{0.47\textwidth}
\begin{equation}
@@ -124,19 +124,19 @@ The consideration of the time discretization and inserting $W_j = 1$ finally lea
V_i \frac{\hat u_i^{n+1} - \hat u_i^{n}}{\Delta t} + \int_{\partial B_i} F(\tilde u^{n+1}) \cdot \mathbf n \; d{\varGamma}_{B_i} - V_i \: q^{n+1} \: = 0
\end{equation}
-\subsection{Cell Centered Finite Volume Method - A short introduction}\label{cc}
+\subsection{Cell centered finite volume method - A short introduction}\label{cc}
\begin{figure} [h]
\centering
\includegraphics[width=0.4\linewidth,keepaspectratio]{EPS/cc_disc}
-\caption{\label{pc:cc} Discretization of the Cell Centered Finite Volume Method}
+\caption{\label{pc:cc} Discretization of the cell centered finite volume method}
\end{figure}
The cell centered finite volume method uses the elements of the grid as control volumes.
For each control volume all discrete values are determined at the element/control volume center (see Figure~\ref{pc:cc}).
The mass or energy fluxes are evaluated at the integration points ($x_{ij}$), which are located at the midpoints of the control
volume faces. This is a two point flux approximation since the flux between the element/control volume centers $i$ and $j$ is calculated
-only with information from these two points. In contrast the BOX-method uses a multi-point flux approximation where all nodes of the
+only with information from these two points. In contrast the box method uses a multi-point flux approximation where all nodes of the
element influence the flux between two specific nodes. \\
Neumann boundary conditions are applied at the boundary control volume faces and Dirichlet boundary conditions at the boundary control volumes. \\
The cell centered finite volume method is robust and mass conservative but should only be applied for structured grids
diff --git a/doc/handbook/structure.tex b/doc/handbook/structure.tex
index 629d9a4b8e..1738473b42 100644
--- a/doc/handbook/structure.tex
+++ b/doc/handbook/structure.tex
@@ -176,7 +176,7 @@ Doxygen documentation should be considered.
\draw (fsys)--(2.4,-7);
\draw [->](c3)--(6.5,9) node [right,text width=12.5cm,align=left]
- {Common files of the implicit (box- and cell-centered) models and the de-\\[-4pt]coupled models: time integration, start routine, the property system, ...};
+ {Common files of the implicit (box and cell centered) models and the de-\\[-4pt]coupled models: time integration, start routine, the property system, ...};
\draw [->](spec3)--(6.5,8) node [right,text width=12.5cm,align=left]
{Specific model definition for the decoupled formulation. In each model \\[-4pt]folder are subdirectories for the implicit pressure equation, sorted by \\[-4pt]discretization method, and for the explicit transport.};
\draw [->](c2)--(6.5,7) node [right,text width=12.5cm,align=left]
@@ -215,6 +215,8 @@ Doxygen documentation should be considered.
\draw [->](para)--(6.5,-10) node [right,text width=12.5cm,align=left]
{Files for parallel programming.};
\end{tikzpicture}
+\caption{Structure of the directory \texttt{dumux} containing the \Dumux source files.}
+\label{fig:dumux-structure}
\end{sidewaysfigure}
% \begin{landscape}
diff --git a/doc/handbook/tutorial.tex b/doc/handbook/tutorial.tex
index 27b305d564..4233c1b56b 100644
--- a/doc/handbook/tutorial.tex
+++ b/doc/handbook/tutorial.tex
@@ -4,7 +4,7 @@ In \Dumux two sorts of models are implemented: Fully-coupled models and decouple
Examples for different kinds of both, coupled and decoupled models, are isothermal two-phase models, isothermal two-phase two-component models, non-isothermal two-phase models and non-isothermal two-phase two-component models.
-In section \ref{box} a short introduction to the box method is given. The box method is used in the fully-coupled models for the spatial discretization of the system of equations. The decoupled models employ usually a cell-centered finite volume scheme. The following two sections of the tutorial demonstrate how to solve problems using, first, a fully-coupled model (section \ref{tutorial-coupled}) and, second, using a decoupled model (section \ref{tutorial-decoupled}). Being the easiest case, an isothermal two-phase system (two fluid phases, one solid phase) will be considered.
+In section \ref{box} a short introduction to the box method is given, in section \ref{cc} the cell centered finite volume method is introduced. The box method is used in the fully-coupled models for the spatial discretization of the system of equations. The decoupled models employ usually a cell centered finite volume scheme. The following two sections of the tutorial demonstrate how to solve problems using, first, a fully-coupled model (section \ref{tutorial-coupled}) and, second, using a decoupled model (section \ref{tutorial-decoupled}). Being the easiest case, an isothermal two-phase system (two fluid phases, one solid phase) will be considered.
\input{tutorial-coupled}
\input{tutorial-decoupled}
%\input{tutorial-newmodel}
--
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