Commit e66c2a35 by Timo Koch

### Merge branch 'cherry-pick-88fb608b' into 'releases/3.0'

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

See merge request !1443
parents 7697a714 fc21c4e5
 ... ... @@ -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 ... ...