start talking about the mesh

tex/diagrams.tex

+%! TEX program = lualatex
+
+\input{.maindir/tex/header/preamble-section}
+% inputs the preamble only if necessary
+\docStart
+\begin{figure}[ht]
+  \centering
+  \tikzinput{Cd}
+  \caption{$C_d$}%
+  \label{fig:Cd}
+\end{figure}
+\begin{figure}[ht]
+  \centering
+  \tikzinput{Cl_f}
+  \caption{$C_l(f)$}%
+  \label{fig:Clf}
+\end{figure}
+\begin{figure}[ht]
+  \centering
+  \tikzinput{Cl_r}
+  \caption{$C_l(r)$}%
+  \label{fig:Clr}
+\end{figure}
+\begin{figure}[ht]
+  \centering
+  \tikzinput{Cl}
+  \caption{$C_l$}%
+  \label{fig:Cl}
+\end{figure}
+\begin{figure}[ht]
+  \centering
+  \tikzinput{Cm}
+  \caption{$C_m$}%
+  \label{fig:Cm}
+\end{figure}
+\begin{figure}[ht]
+  \centering
+  \tikzinput{0}
+  \caption{pressure in front of the cylinder}%
+  \label{fig:0}
+\end{figure}
+\begin{figure}[ht]
+  \centering
+  \tikzinput{1}
+  \caption{pressure behind the cylinder}%
+  \label{fig:1}
+\end{figure}
+\begin{figure}[ht]
+  \centering
+  \tikzinput{p_diff}
+  \caption{pressure difference}%
+  \label{fig:1}
+\end{figure}
+\begin{figure}[ht]
+  \centering
+  \tikzinput{bothpressures}
+  \caption{Pressure in front and behind the cylinder}%
+  \label{fig:bothPressures}
+\end{figure}
+\docEnd

tex/header/preamble.tex

@@ -15,6 +15,11 @@
 \WarningFilter{latex}{You have requested package `.maindir/tex/header/}
 
 \usepackage[tikz]{.maindir/tex/header/stdmath} % , scriptLetters
+\usepackage{pgfplots}
+
+\usepackage{listings}
+\lstMakeShortInline[columns=fixed]|
+\usepackage[section]{placeins}  % makes sure that the figures stay within their section
 
 \setmainfont{Latin Modern Roman}
 \setsansfont{Latin Modern Sans}
@@ -34,6 +39,7 @@
   pdfencoding=auto
 }
 % Abkürzunngen
+\newcommand{\diagramwidth}{0.9\linewidth}
 
 % weitere Befehle
 

tex/header/stdmath.sty

@@ -51,7 +51,7 @@
 \ProcessOptions\relax
 
 \ifopt@pics\RequirePackage{graphicx}\fi
-\ifopt@tikz\RequirePackage{tikz}\RequirePackage{tikz-cd}\RequirePackage{pgfplots}\fi
+\ifopt@tikz\RequirePackage{tikz}\RequirePackage{tikz-cd}\RequirePackage{pgfplots}\pgfplotsset{compat=1.17}\fi
 \ifopt@script\RequirePackage{mathrsfs}\newcommand{\scr}[1]{\mathscr{#1}}\fi % for script A (sigma-Algebra-A)
 
 % ---------
@@ -72,7 +72,7 @@
 % with \overset{\text{Definition}}&{=} instead of &\stackrel{\text{Definition}}=
 \RequirePackage{mathtools}    % for := (defined as)
 \RequirePackage{amsthm}                   % for theorems environments
-\RequirePackage{microtype}   % should improve typesetting, sometimes removing underfull hboxes
+% \RequirePackage{microtype}   % should improve typesetting, sometimes removing underfull hboxes
 \RequirePackage{enumerate}                  % for different kind of numbering in enumerations
 \RequirePackage[version=4]{mhchem}  % chemical formulars. Provides \ce
 \RequirePackage[per-mode=fraction,

tex/main.tex

@@ -5,8 +5,10 @@
 \author{Felix Hilsky}
 \maketitle
 % use \textinput as described in /header and _TEMPLATE
-\begin{appendices}
+\textinput{mesh}
+\textinput{diagrams}
+% \begin{appendices}
   % \textinput{some-appendix-section}
-\end{appendices}
+% \end{appendices}
 % use \textinput as described in /header and _TEMPLATE
 \docEnd

tex/mesh.tex

+%! TEX program = lualatex
+
+\input{.maindir/tex/header/preamble-section}
+% inputs the preamble only if necessary
+\docStart
+\section{Mesh}
+
+For the mesh the domain was divided into 5 subdomains.
+One subdomain consists of the \SI{1.8}{\metre} on the side of the outlet without the cylinder.
+On this part (called \enquote{pipe}) the grading is chosen in a way that the cells closest to the cylinder are smaller than those at the outlet and almost of the same size as the neigboring cells in the neigboring subdomain.
+
+The area around the cylinder is divided into four quarters, each with a quarter of the cylinder and one boundary part as boundaries.
+The grading is chosen in a way that the cells closest to the cylinder are smallest and all cells are quite close to squares. (|Max-aspect-ratio = 2.4|)
+Since each of the four quarters dictates the number and grading of the cells in radius direction to its neighbors, all four quarters have the same number in this direction even though the cylinder is not perfectly in the center between the walls.
+In the corners of the area around the cylinder the angle of the outermost cells are \SI{45}{°}. I could not find a way to improve this, but |checkMesh| calls the mesh \enquote{OK}.
+
+\begin{figure}[htpb]
+  \centering
+  \includegraphics[width=0.8\linewidth]{.maindir/zeichnungen/meshN8}
+  \caption{The mesh for $N = 8$. With $2$ correctors, $N=8$ does not work (Courant number blows up), but with $4$ correctors, it does work.}%
+  \label{fig:mesh}
+\end{figure}
+\docEnd