Commit fc21c4e5 authored by Timo Koch's avatar Timo Koch

Merge branch 'fix/handbook-numerics' into 'master'

Fix/handbook numerics

See merge request !1442

(cherry picked from commit 88fb608b)

79f8e95a [doc][handbook] each matrix entry is related to control volume
1b490505 [doc][handbook] more than one cc scheme is available now
4d279858 [doc][handbook] use pdf for interaction volume pic
fcb797eb [doc][handbook] remove duplicate word
parent 7697a714
......@@ -50,8 +50,8 @@ direction of maximum growth $\textbf{x}^i$ until our approximated solution becom
\subsection{Structure of matrix and vectors}
To understand the meaning of an entry in the matrix or the vector of the linear system, we have
to define their structure. Both have a blocking structure. Each block contains the degrees of
freedom (also called variable or unknown) for a sub-control volume. The equation index is used
to order of the degrees of freedom. For each sub-control volume we have one block. The mapper is
freedom (also called variable or unknown) for a control volume. The equation index is used
to order of the degrees of freedom. For each control volume we have one block. The mapper is
used to order the blocks.
\begin{figure}[htbp]
......@@ -59,23 +59,23 @@ used to order the blocks.
\begin{tikzpicture}[fill=dumuxBlue]
%% blocking structure
% matrix
\node at (0.3,4.2){\footnotesize 1. SCV};
\node at (1.7,4.2){\footnotesize 2. SCV};
\node at (3.5,4.2){\footnotesize $n$. SCV};
\node at (0.3,4.2){\footnotesize 1. CV};
\node at (1.7,4.2){\footnotesize 2. CV};
\node at (3.5,4.2){\footnotesize $n$. CV};
\draw (0,0) rectangle (4,4);
\fill (0.1,3.1) rectangle (0.9,3.9);
\fill (1.1,3.1) rectangle (1.9,3.9);
\node at (2.5,3.5) {$\dots$};
\fill (3.1,3.1) rectangle (3.9,3.9);
\node at (4,3.5) [right]{\footnotesize 1. SCV};
\node at (4,3.5) [right]{\footnotesize 1. CV};
\fill (0.1,2.1) rectangle (0.9,2.9);
\fill (1.1,2.1) rectangle (1.9,2.9);
\node at (2.5,2.5) {$\dots$};
\fill (3.1,2.1) rectangle (3.9,2.9);
\node at (4,2.5) [right]{\footnotesize 2. SCV};
\node at (4,2.5) [right]{\footnotesize 2. CV};
\node at (0.5,1.5) {$\vdots$};
\node at (1.5,1.5) {$\vdots$};
......@@ -86,7 +86,7 @@ used to order the blocks.
\fill (1.1,0.1) rectangle (1.9,0.9);
\node at (2.5,0.5) {$\dots$};
\fill (3.1,0.1) rectangle (3.9,0.9);
\node at (4,0.5) [right]{\footnotesize $n$. SCV};
\node at (4,0.5) [right]{\footnotesize $n$. CV};
% vector
\draw (5.5,0) rectangle (5.9,4);
......@@ -94,19 +94,19 @@ used to order the blocks.
\fill (5.6,2.1) rectangle (5.8,2.9);
\node at (5.7,1.5) {$\vdots$};
\fill (5.6,0.1) rectangle (5.8,0.9);
%% intra-block structure
\fill (8.1,2.1) rectangle (8.9,2.9);
\draw (9,2.8) -- (9.6,3.4);
\draw (9,2.6) -- (9.6,2.8);
\draw (9,2.2) -- (9.3,1.6);
\node at (10,4) {${eqIdx}$};
\node at (10,3.4) {$0$};
\node at (10,2.8) {$1$};
\node at (10,2.2) {$\vdots$};
\node at (10,1.6) {$m-1$};
\fill (11.1,2.1) rectangle (11.3,2.9);
\draw (11,2.8) -- (10.4,3.4);
\draw (11,2.6) -- (10.4,2.8);
......
\section{Spatial Discretization Schemes}
\label{spatialdiscretization}
We discretize space with the cell-centered finite volume method (\ref{cc} ), the box method (\ref{box})
We discretize space with cell-centered finite volume methods (\ref{cc} ), the box method (\ref{box})
or a staggered grid scheme.
Grid adaption is available for both box and cell-centered finite volume method.
In general, the spatial parameters, especially the porosity, have to be assigned on
......@@ -271,7 +271,7 @@ Using these conditions, the intermediate face unknowns ${u}_\sigma$ can be elimi
\begin{figure} [ht]
\centering
\includegraphics[width=0.8\linewidth,keepaspectratio]{png/mpfa_iv.png}
\includegraphics[width=0.8\linewidth,keepaspectratio]{pdf/mpfa_iv.pdf}
\caption{Interaction region for the Mpfa-O method. The graphic on the right illustrates how the sub-control volume $L^v$ and face $\sigma^v_2$ are embedded in cell $L$. Note that the face stencils for all sub-control volume faces in the depicted interaction region are $\mathcal{S}_{\sigma^v_i} = \{ K,L,M \}$, meaning that the fluxes over the sub-control volume faces depend on the three cell unknowns $u_K, u_L, u_M$.}
\label{pc:interactionRegion_mpfa}
\end{figure}
......
......@@ -13,7 +13,7 @@ point of view.
\label{content}
In Figure \ref{fig:algorithm}, the algorithmic representations of a monolithical
solution solution scheme is illustrated down to the element level.
solution scheme is illustrated down to the element level.
\begin{figure}[hbt]
\setcounter{thingCounter}{0}
......
......@@ -30,7 +30,7 @@ set(TEX_IMAGES
png/dalton1.png
png/dalton2.png
pdf/staggered_grid.pdf
png/mpfa_iv.png)
pdf/mpfa_iv.pdf)
dune_add_latex_document(0_dumux-handbook.tex
BIBFILES dumux-handbook.bib
......
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