m2cce/openfoam_project
Archived
1
Fork 0
Code Issues Pull requests Projects Releases Wiki Activity

Report: Method

Browse source
This commit is contained in:
Edgar P. Burkhart 2022-01-31 17:13:18 +01:00
parent 417a6640c4
commit 70a4e4bb59
Signed by: edpibu
GPG key ID: 9833D3C5A25BD227
5 changed files with 2899 additions and 16 deletions
Show stats Download patch file Download diff file Expand all files Collapse all files

1
report/cours.sty
View file

@ -115,6 +115,7 @@
\DeclareMathOperator\cond{cond}
\DeclareMathOperator\erf{erf}
\DeclareMathOperator\erfc{erfc}
\DeclareMathOperator\sech{sech}
%%% Vecteurs et Matrices
\renewcommand\u[1]{\underline{#1}}

684
report/fig/bathy.pgf Normal file
View file

@ -0,0 +1,684 @@
%% Creator: Matplotlib, PGF backend
%%
%% To include the figure in your LaTeX document, write
%% \input{<filename>.pgf}
%%
%% Make sure the required packages are loaded in your preamble
%% \usepackage{pgf}
%%
%% Also ensure that all the required font packages are loaded; for instance,
%% the lmodern package is sometimes necessary when using math font.
%% \usepackage{lmodern}
%%
%% Figures using additional raster images can only be included by \input if
%% they are in the same directory as the main LaTeX file. For loading figures
%% from other directories you can use the `import` package
%% \usepackage{import}
%%
%% and then include the figures with
%% \import{<path to file>}{<filename>.pgf}
%%
%% Matplotlib used the following preamble
%% \usepackage{fontspec}
%% \setmainfont{DejaVuSerif.ttf}[Path=\detokenize{/home/edpibu/Code/openfoam_project/env/lib/python3.10/site-packages/matplotlib/mpl-data/fonts/ttf/}]
%% \setsansfont{DejaVuSans.ttf}[Path=\detokenize{/home/edpibu/Code/openfoam_project/env/lib/python3.10/site-packages/matplotlib/mpl-data/fonts/ttf/}]
%% \setmonofont{DejaVuSansMono.ttf}[Path=\detokenize{/home/edpibu/Code/openfoam_project/env/lib/python3.10/site-packages/matplotlib/mpl-data/fonts/ttf/}]
%%
\begingroup%
\makeatletter%
\begin{pgfpicture}%
\pgfpathrectangle{\pgfpointorigin}{\pgfqpoint{6.000000in}{2.000000in}}%
\pgfusepath{use as bounding box, clip}%
\begin{pgfscope}%
\pgfsetbuttcap%
\pgfsetmiterjoin%
\definecolor{currentfill}{rgb}{1.000000,1.000000,1.000000}%
\pgfsetfillcolor{currentfill}%
\pgfsetlinewidth{0.000000pt}%
\definecolor{currentstroke}{rgb}{1.000000,1.000000,1.000000}%
\pgfsetstrokecolor{currentstroke}%
\pgfsetdash{}{0pt}%
\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}%
\pgfpathlineto{\pgfqpoint{6.000000in}{0.000000in}}%
\pgfpathlineto{\pgfqpoint{6.000000in}{2.000000in}}%
\pgfpathlineto{\pgfqpoint{0.000000in}{2.000000in}}%
\pgfpathlineto{\pgfqpoint{0.000000in}{0.000000in}}%
\pgfpathclose%
\pgfusepath{fill}%
\end{pgfscope}%
\begin{pgfscope}%
\pgfsetbuttcap%
\pgfsetmiterjoin%
\definecolor{currentfill}{rgb}{1.000000,1.000000,1.000000}%
\pgfsetfillcolor{currentfill}%
\pgfsetlinewidth{0.000000pt}%
\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
\pgfsetstrokecolor{currentstroke}%
\pgfsetstrokeopacity{0.000000}%
\pgfsetdash{}{0pt}%
\pgfpathmoveto{\pgfqpoint{0.750000in}{0.571935in}}%
\pgfpathlineto{\pgfqpoint{5.400000in}{0.571935in}}%
\pgfpathlineto{\pgfqpoint{5.400000in}{1.408065in}}%
\pgfpathlineto{\pgfqpoint{0.750000in}{1.408065in}}%
\pgfpathlineto{\pgfqpoint{0.750000in}{0.571935in}}%
\pgfpathclose%
\pgfusepath{fill}%
\end{pgfscope}%
\begin{pgfscope}%
\pgfpathrectangle{\pgfqpoint{0.750000in}{0.571935in}}{\pgfqpoint{4.650000in}{0.836130in}}%
\pgfusepath{clip}%
\pgfsetrectcap%
\pgfsetroundjoin%
\pgfsetlinewidth{0.803000pt}%
\definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}%
\pgfsetstrokecolor{currentstroke}%
\pgfsetdash{}{0pt}%
\pgfpathmoveto{\pgfqpoint{0.750000in}{0.571935in}}%
\pgfpathlineto{\pgfqpoint{0.750000in}{1.408065in}}%
\pgfusepath{stroke}%
\end{pgfscope}%
\begin{pgfscope}%
\pgfsetbuttcap%
\pgfsetroundjoin%
\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
\pgfsetfillcolor{currentfill}%
\pgfsetlinewidth{0.803000pt}%
\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
\pgfsetstrokecolor{currentstroke}%
\pgfsetdash{}{0pt}%
\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{%
\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}%
\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}%
\pgfusepath{stroke,fill}%
}%
\begin{pgfscope}%
\pgfsys@transformshift{0.750000in}{0.571935in}%
\pgfsys@useobject{currentmarker}{}%
\end{pgfscope}%
\end{pgfscope}%
\begin{pgfscope}%
\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
\pgfsetstrokecolor{textcolor}%
\pgfsetfillcolor{textcolor}%
\pgftext[x=0.750000in,y=0.474713in,,top]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont 0}%
\end{pgfscope}%
\begin{pgfscope}%
\pgfpathrectangle{\pgfqpoint{0.750000in}{0.571935in}}{\pgfqpoint{4.650000in}{0.836130in}}%
\pgfusepath{clip}%
\pgfsetrectcap%
\pgfsetroundjoin%
\pgfsetlinewidth{0.803000pt}%
\definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}%
\pgfsetstrokecolor{currentstroke}%
\pgfsetdash{}{0pt}%
\pgfpathmoveto{\pgfqpoint{1.370000in}{0.571935in}}%
\pgfpathlineto{\pgfqpoint{1.370000in}{1.408065in}}%
\pgfusepath{stroke}%
\end{pgfscope}%
\begin{pgfscope}%
\pgfsetbuttcap%
\pgfsetroundjoin%
\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
\pgfsetfillcolor{currentfill}%
\pgfsetlinewidth{0.803000pt}%
\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
\pgfsetstrokecolor{currentstroke}%
\pgfsetdash{}{0pt}%
\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{%
\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}%
\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}%
\pgfusepath{stroke,fill}%
}%
\begin{pgfscope}%
\pgfsys@transformshift{1.370000in}{0.571935in}%
\pgfsys@useobject{currentmarker}{}%
\end{pgfscope}%
\end{pgfscope}%
\begin{pgfscope}%
\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
\pgfsetstrokecolor{textcolor}%
\pgfsetfillcolor{textcolor}%
\pgftext[x=1.370000in,y=0.474713in,,top]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont 20}%
\end{pgfscope}%
\begin{pgfscope}%
\pgfpathrectangle{\pgfqpoint{0.750000in}{0.571935in}}{\pgfqpoint{4.650000in}{0.836130in}}%
\pgfusepath{clip}%
\pgfsetrectcap%
\pgfsetroundjoin%
\pgfsetlinewidth{0.803000pt}%
\definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}%
\pgfsetstrokecolor{currentstroke}%
\pgfsetdash{}{0pt}%
\pgfpathmoveto{\pgfqpoint{1.990000in}{0.571935in}}%
\pgfpathlineto{\pgfqpoint{1.990000in}{1.408065in}}%
\pgfusepath{stroke}%
\end{pgfscope}%
\begin{pgfscope}%
\pgfsetbuttcap%
\pgfsetroundjoin%
\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
\pgfsetfillcolor{currentfill}%
\pgfsetlinewidth{0.803000pt}%
\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
\pgfsetstrokecolor{currentstroke}%
\pgfsetdash{}{0pt}%
\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{%
\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}%
\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}%
\pgfusepath{stroke,fill}%
}%
\begin{pgfscope}%
\pgfsys@transformshift{1.990000in}{0.571935in}%
\pgfsys@useobject{currentmarker}{}%
\end{pgfscope}%
\end{pgfscope}%
\begin{pgfscope}%
\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
\pgfsetstrokecolor{textcolor}%
\pgfsetfillcolor{textcolor}%
\pgftext[x=1.990000in,y=0.474713in,,top]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont 40}%
\end{pgfscope}%
\begin{pgfscope}%
\pgfpathrectangle{\pgfqpoint{0.750000in}{0.571935in}}{\pgfqpoint{4.650000in}{0.836130in}}%
\pgfusepath{clip}%
\pgfsetrectcap%
\pgfsetroundjoin%
\pgfsetlinewidth{0.803000pt}%
\definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}%
\pgfsetstrokecolor{currentstroke}%
\pgfsetdash{}{0pt}%
\pgfpathmoveto{\pgfqpoint{2.610000in}{0.571935in}}%
\pgfpathlineto{\pgfqpoint{2.610000in}{1.408065in}}%
\pgfusepath{stroke}%
\end{pgfscope}%
\begin{pgfscope}%
\pgfsetbuttcap%
\pgfsetroundjoin%
\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
\pgfsetfillcolor{currentfill}%
\pgfsetlinewidth{0.803000pt}%
\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
\pgfsetstrokecolor{currentstroke}%
\pgfsetdash{}{0pt}%
\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{%
\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}%
\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}%
\pgfusepath{stroke,fill}%
}%
\begin{pgfscope}%
\pgfsys@transformshift{2.610000in}{0.571935in}%
\pgfsys@useobject{currentmarker}{}%
\end{pgfscope}%
\end{pgfscope}%
\begin{pgfscope}%
\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
\pgfsetstrokecolor{textcolor}%
\pgfsetfillcolor{textcolor}%
\pgftext[x=2.610000in,y=0.474713in,,top]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont 60}%
\end{pgfscope}%
\begin{pgfscope}%
\pgfpathrectangle{\pgfqpoint{0.750000in}{0.571935in}}{\pgfqpoint{4.650000in}{0.836130in}}%
\pgfusepath{clip}%
\pgfsetrectcap%
\pgfsetroundjoin%
\pgfsetlinewidth{0.803000pt}%
\definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}%
\pgfsetstrokecolor{currentstroke}%
\pgfsetdash{}{0pt}%
\pgfpathmoveto{\pgfqpoint{3.230000in}{0.571935in}}%
\pgfpathlineto{\pgfqpoint{3.230000in}{1.408065in}}%
\pgfusepath{stroke}%
\end{pgfscope}%
\begin{pgfscope}%
\pgfsetbuttcap%
\pgfsetroundjoin%
\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
\pgfsetfillcolor{currentfill}%
\pgfsetlinewidth{0.803000pt}%
\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
\pgfsetstrokecolor{currentstroke}%
\pgfsetdash{}{0pt}%
\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{%
\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}%
\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}%
\pgfusepath{stroke,fill}%
}%
\begin{pgfscope}%
\pgfsys@transformshift{3.230000in}{0.571935in}%
\pgfsys@useobject{currentmarker}{}%
\end{pgfscope}%
\end{pgfscope}%
\begin{pgfscope}%
\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
\pgfsetstrokecolor{textcolor}%
\pgfsetfillcolor{textcolor}%
\pgftext[x=3.230000in,y=0.474713in,,top]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont 80}%
\end{pgfscope}%
\begin{pgfscope}%
\pgfpathrectangle{\pgfqpoint{0.750000in}{0.571935in}}{\pgfqpoint{4.650000in}{0.836130in}}%
\pgfusepath{clip}%
\pgfsetrectcap%
\pgfsetroundjoin%
\pgfsetlinewidth{0.803000pt}%
\definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}%
\pgfsetstrokecolor{currentstroke}%
\pgfsetdash{}{0pt}%
\pgfpathmoveto{\pgfqpoint{3.850000in}{0.571935in}}%
\pgfpathlineto{\pgfqpoint{3.850000in}{1.408065in}}%
\pgfusepath{stroke}%
\end{pgfscope}%
\begin{pgfscope}%
\pgfsetbuttcap%
\pgfsetroundjoin%
\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
\pgfsetfillcolor{currentfill}%
\pgfsetlinewidth{0.803000pt}%
\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
\pgfsetstrokecolor{currentstroke}%
\pgfsetdash{}{0pt}%
\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{%
\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}%
\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}%
\pgfusepath{stroke,fill}%
}%
\begin{pgfscope}%
\pgfsys@transformshift{3.850000in}{0.571935in}%
\pgfsys@useobject{currentmarker}{}%
\end{pgfscope}%
\end{pgfscope}%
\begin{pgfscope}%
\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
\pgfsetstrokecolor{textcolor}%
\pgfsetfillcolor{textcolor}%
\pgftext[x=3.850000in,y=0.474713in,,top]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont 100}%
\end{pgfscope}%
\begin{pgfscope}%
\pgfpathrectangle{\pgfqpoint{0.750000in}{0.571935in}}{\pgfqpoint{4.650000in}{0.836130in}}%
\pgfusepath{clip}%
\pgfsetrectcap%
\pgfsetroundjoin%
\pgfsetlinewidth{0.803000pt}%
\definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}%
\pgfsetstrokecolor{currentstroke}%
\pgfsetdash{}{0pt}%
\pgfpathmoveto{\pgfqpoint{4.470000in}{0.571935in}}%
\pgfpathlineto{\pgfqpoint{4.470000in}{1.408065in}}%
\pgfusepath{stroke}%
\end{pgfscope}%
\begin{pgfscope}%
\pgfsetbuttcap%
\pgfsetroundjoin%
\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
\pgfsetfillcolor{currentfill}%
\pgfsetlinewidth{0.803000pt}%
\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
\pgfsetstrokecolor{currentstroke}%
\pgfsetdash{}{0pt}%
\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{%
\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}%
\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}%
\pgfusepath{stroke,fill}%
}%
\begin{pgfscope}%
\pgfsys@transformshift{4.470000in}{0.571935in}%
\pgfsys@useobject{currentmarker}{}%
\end{pgfscope}%
\end{pgfscope}%
\begin{pgfscope}%
\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
\pgfsetstrokecolor{textcolor}%
\pgfsetfillcolor{textcolor}%
\pgftext[x=4.470000in,y=0.474713in,,top]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont 120}%
\end{pgfscope}%
\begin{pgfscope}%
\pgfpathrectangle{\pgfqpoint{0.750000in}{0.571935in}}{\pgfqpoint{4.650000in}{0.836130in}}%
\pgfusepath{clip}%
\pgfsetrectcap%
\pgfsetroundjoin%
\pgfsetlinewidth{0.803000pt}%
\definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}%
\pgfsetstrokecolor{currentstroke}%
\pgfsetdash{}{0pt}%
\pgfpathmoveto{\pgfqpoint{5.090000in}{0.571935in}}%
\pgfpathlineto{\pgfqpoint{5.090000in}{1.408065in}}%
\pgfusepath{stroke}%
\end{pgfscope}%
\begin{pgfscope}%
\pgfsetbuttcap%
\pgfsetroundjoin%
\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
\pgfsetfillcolor{currentfill}%
\pgfsetlinewidth{0.803000pt}%
\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
\pgfsetstrokecolor{currentstroke}%
\pgfsetdash{}{0pt}%
\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{%
\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}%
\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}%
\pgfusepath{stroke,fill}%
}%
\begin{pgfscope}%
\pgfsys@transformshift{5.090000in}{0.571935in}%
\pgfsys@useobject{currentmarker}{}%
\end{pgfscope}%
\end{pgfscope}%
\begin{pgfscope}%
\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
\pgfsetstrokecolor{textcolor}%
\pgfsetfillcolor{textcolor}%
\pgftext[x=5.090000in,y=0.474713in,,top]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont 140}%
\end{pgfscope}%
\begin{pgfscope}%
\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
\pgfsetstrokecolor{textcolor}%
\pgfsetfillcolor{textcolor}%
\pgftext[x=3.075000in,y=0.284744in,,top]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont x (m)}%
\end{pgfscope}%
\begin{pgfscope}%
\pgfpathrectangle{\pgfqpoint{0.750000in}{0.571935in}}{\pgfqpoint{4.650000in}{0.836130in}}%
\pgfusepath{clip}%
\pgfsetrectcap%
\pgfsetroundjoin%
\pgfsetlinewidth{0.803000pt}%
\definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}%
\pgfsetstrokecolor{currentstroke}%
\pgfsetdash{}{0pt}%
\pgfpathmoveto{\pgfqpoint{0.750000in}{0.805859in}}%
\pgfpathlineto{\pgfqpoint{5.400000in}{0.805859in}}%
\pgfusepath{stroke}%
\end{pgfscope}%
\begin{pgfscope}%
\pgfsetbuttcap%
\pgfsetroundjoin%
\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
\pgfsetfillcolor{currentfill}%
\pgfsetlinewidth{0.803000pt}%
\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
\pgfsetstrokecolor{currentstroke}%
\pgfsetdash{}{0pt}%
\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.048611in}{0.000000in}}{\pgfqpoint{-0.000000in}{0.000000in}}{%
\pgfpathmoveto{\pgfqpoint{-0.000000in}{0.000000in}}%
\pgfpathlineto{\pgfqpoint{-0.048611in}{0.000000in}}%
\pgfusepath{stroke,fill}%
}%
\begin{pgfscope}%
\pgfsys@transformshift{0.750000in}{0.805859in}%
\pgfsys@useobject{currentmarker}{}%
\end{pgfscope}%
\end{pgfscope}%
\begin{pgfscope}%
\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
\pgfsetstrokecolor{textcolor}%
\pgfsetfillcolor{textcolor}%
\pgftext[x=0.368022in, y=0.753098in, left, base]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont \ensuremath{-}10}%
\end{pgfscope}%
\begin{pgfscope}%
\pgfpathrectangle{\pgfqpoint{0.750000in}{0.571935in}}{\pgfqpoint{4.650000in}{0.836130in}}%
\pgfusepath{clip}%
\pgfsetrectcap%
\pgfsetroundjoin%
\pgfsetlinewidth{0.803000pt}%
\definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}%
\pgfsetstrokecolor{currentstroke}%
\pgfsetdash{}{0pt}%
\pgfpathmoveto{\pgfqpoint{0.750000in}{1.115859in}}%
\pgfpathlineto{\pgfqpoint{5.400000in}{1.115859in}}%
\pgfusepath{stroke}%
\end{pgfscope}%
\begin{pgfscope}%
\pgfsetbuttcap%
\pgfsetroundjoin%
\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
\pgfsetfillcolor{currentfill}%
\pgfsetlinewidth{0.803000pt}%
\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
\pgfsetstrokecolor{currentstroke}%
\pgfsetdash{}{0pt}%
\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.048611in}{0.000000in}}{\pgfqpoint{-0.000000in}{0.000000in}}{%
\pgfpathmoveto{\pgfqpoint{-0.000000in}{0.000000in}}%
\pgfpathlineto{\pgfqpoint{-0.048611in}{0.000000in}}%
\pgfusepath{stroke,fill}%
}%
\begin{pgfscope}%
\pgfsys@transformshift{0.750000in}{1.115859in}%
\pgfsys@useobject{currentmarker}{}%
\end{pgfscope}%
\end{pgfscope}%
\begin{pgfscope}%
\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
\pgfsetstrokecolor{textcolor}%
\pgfsetfillcolor{textcolor}%
\pgftext[x=0.564412in, y=1.063098in, left, base]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont 0}%
\end{pgfscope}%
\begin{pgfscope}%
\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
\pgfsetstrokecolor{textcolor}%
\pgfsetfillcolor{textcolor}%
\pgftext[x=0.312467in,y=0.990000in,,bottom,rotate=90.000000]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont y (m)}%
\end{pgfscope}%
\begin{pgfscope}%
\pgfsetrectcap%
\pgfsetmiterjoin%
\pgfsetlinewidth{0.803000pt}%
\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
\pgfsetstrokecolor{currentstroke}%
\pgfsetdash{}{0pt}%
\pgfpathmoveto{\pgfqpoint{0.750000in}{0.571935in}}%
\pgfpathlineto{\pgfqpoint{0.750000in}{1.408065in}}%
\pgfusepath{stroke}%
\end{pgfscope}%
\begin{pgfscope}%
\pgfsetrectcap%
\pgfsetmiterjoin%
\pgfsetlinewidth{0.803000pt}%
\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
\pgfsetstrokecolor{currentstroke}%
\pgfsetdash{}{0pt}%
\pgfpathmoveto{\pgfqpoint{5.400000in}{0.571935in}}%
\pgfpathlineto{\pgfqpoint{5.400000in}{1.408065in}}%
\pgfusepath{stroke}%
\end{pgfscope}%
\begin{pgfscope}%
\pgfsetrectcap%
\pgfsetmiterjoin%
\pgfsetlinewidth{0.803000pt}%
\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
\pgfsetstrokecolor{currentstroke}%
\pgfsetdash{}{0pt}%
\pgfpathmoveto{\pgfqpoint{0.750000in}{0.571935in}}%
\pgfpathlineto{\pgfqpoint{5.400000in}{0.571935in}}%
\pgfusepath{stroke}%
\end{pgfscope}%
\begin{pgfscope}%
\pgfsetrectcap%
\pgfsetmiterjoin%
\pgfsetlinewidth{0.803000pt}%
\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
\pgfsetstrokecolor{currentstroke}%
\pgfsetdash{}{0pt}%
\pgfpathmoveto{\pgfqpoint{0.750000in}{1.408065in}}%
\pgfpathlineto{\pgfqpoint{5.400000in}{1.408065in}}%
\pgfusepath{stroke}%
\end{pgfscope}%
\begin{pgfscope}%
\pgfsetbuttcap%
\pgfsetmiterjoin%
\definecolor{currentfill}{rgb}{1.000000,1.000000,1.000000}%
\pgfsetfillcolor{currentfill}%
\pgfsetfillopacity{0.800000}%
\pgfsetlinewidth{1.003750pt}%
\definecolor{currentstroke}{rgb}{0.800000,0.800000,0.800000}%
\pgfsetstrokecolor{currentstroke}%
\pgfsetstrokeopacity{0.800000}%
\pgfsetdash{}{0pt}%
\pgfpathmoveto{\pgfqpoint{0.847222in}{0.889240in}}%
\pgfpathlineto{\pgfqpoint{2.111233in}{0.889240in}}%
\pgfpathquadraticcurveto{\pgfqpoint{2.139011in}{0.889240in}}{\pgfqpoint{2.139011in}{0.917017in}}%
\pgfpathlineto{\pgfqpoint{2.139011in}{1.310843in}}%
\pgfpathquadraticcurveto{\pgfqpoint{2.139011in}{1.338621in}}{\pgfqpoint{2.111233in}{1.338621in}}%
\pgfpathlineto{\pgfqpoint{0.847222in}{1.338621in}}%
\pgfpathquadraticcurveto{\pgfqpoint{0.819444in}{1.338621in}}{\pgfqpoint{0.819444in}{1.310843in}}%
\pgfpathlineto{\pgfqpoint{0.819444in}{0.917017in}}%
\pgfpathquadraticcurveto{\pgfqpoint{0.819444in}{0.889240in}}{\pgfqpoint{0.847222in}{0.889240in}}%
\pgfpathlineto{\pgfqpoint{0.847222in}{0.889240in}}%
\pgfpathclose%
\pgfusepath{stroke,fill}%
\end{pgfscope}%
\begin{pgfscope}%
\pgfsetrectcap%
\pgfsetroundjoin%
\pgfsetlinewidth{1.003750pt}%
\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
\pgfsetstrokecolor{currentstroke}%
\pgfsetdash{}{0pt}%
\pgfpathmoveto{\pgfqpoint{0.875000in}{1.226153in}}%
\pgfpathlineto{\pgfqpoint{1.013889in}{1.226153in}}%
\pgfpathlineto{\pgfqpoint{1.152778in}{1.226153in}}%
\pgfusepath{stroke}%
\end{pgfscope}%
\begin{pgfscope}%
\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
\pgfsetstrokecolor{textcolor}%
\pgfsetfillcolor{textcolor}%
\pgftext[x=1.263889in,y=1.177542in,left,base]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont Bathymetry}%
\end{pgfscope}%
\begin{pgfscope}%
\pgfsetrectcap%
\pgfsetroundjoin%
\pgfsetlinewidth{1.003750pt}%
\definecolor{currentstroke}{rgb}{1.000000,0.000000,0.000000}%
\pgfsetstrokecolor{currentstroke}%
\pgfsetdash{}{0pt}%
\pgfpathmoveto{\pgfqpoint{0.875000in}{1.022296in}}%
\pgfpathlineto{\pgfqpoint{1.013889in}{1.022296in}}%
\pgfpathlineto{\pgfqpoint{1.152778in}{1.022296in}}%
\pgfusepath{stroke}%
\end{pgfscope}%
\begin{pgfscope}%
\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
\pgfsetstrokecolor{textcolor}%
\pgfsetfillcolor{textcolor}%
\pgftext[x=1.263889in,y=0.973685in,left,base]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont Armour}%
\end{pgfscope}%
\begin{pgfscope}%
\pgfpathrectangle{\pgfqpoint{0.750000in}{0.571935in}}{\pgfqpoint{4.650000in}{0.836130in}}%
\pgfusepath{clip}%
\pgfsetrectcap%
\pgfsetroundjoin%
\pgfsetlinewidth{1.003750pt}%
\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
\pgfsetstrokecolor{currentstroke}%
\pgfsetdash{}{0pt}%
\pgfpathmoveto{\pgfqpoint{0.750000in}{0.626923in}}%
\pgfpathlineto{\pgfqpoint{0.836364in}{0.628305in}}%
\pgfpathlineto{\pgfqpoint{1.127273in}{0.616420in}}%
\pgfpathlineto{\pgfqpoint{1.527273in}{0.610516in}}%
\pgfpathlineto{\pgfqpoint{1.836364in}{0.650483in}}%
\pgfpathlineto{\pgfqpoint{2.155455in}{0.651658in}}%
\pgfpathlineto{\pgfqpoint{2.537273in}{0.702133in}}%
\pgfpathlineto{\pgfqpoint{2.560000in}{0.709562in}}%
\pgfpathlineto{\pgfqpoint{3.241818in}{0.941031in}}%
\pgfpathlineto{\pgfqpoint{3.505455in}{1.003601in}}%
\pgfpathlineto{\pgfqpoint{3.955455in}{1.100064in}}%
\pgfpathlineto{\pgfqpoint{4.228182in}{1.169342in}}%
\pgfpathlineto{\pgfqpoint{4.469091in}{1.210476in}}%
\pgfpathlineto{\pgfqpoint{4.472727in}{1.195780in}}%
\pgfpathlineto{\pgfqpoint{5.031818in}{1.033995in}}%
\pgfpathlineto{\pgfqpoint{5.136364in}{1.013050in}}%
\pgfpathlineto{\pgfqpoint{5.400000in}{0.958309in}}%
\pgfpathlineto{\pgfqpoint{5.400000in}{0.958309in}}%
\pgfusepath{stroke}%
\end{pgfscope}%
\begin{pgfscope}%
\pgfpathrectangle{\pgfqpoint{0.750000in}{0.571935in}}{\pgfqpoint{4.650000in}{0.836130in}}%
\pgfusepath{clip}%
\pgfsetrectcap%
\pgfsetroundjoin%
\pgfsetlinewidth{1.003750pt}%
\definecolor{currentstroke}{rgb}{1.000000,0.000000,0.000000}%
\pgfsetstrokecolor{currentstroke}%
\pgfsetdash{}{0pt}%
\pgfpathmoveto{\pgfqpoint{1.840909in}{0.651071in}}%
\pgfpathlineto{\pgfqpoint{2.227273in}{0.702133in}}%
\pgfpathlineto{\pgfqpoint{2.250000in}{0.709562in}}%
\pgfpathlineto{\pgfqpoint{2.931818in}{0.941031in}}%
\pgfpathlineto{\pgfqpoint{3.195455in}{1.003601in}}%
\pgfpathlineto{\pgfqpoint{3.645455in}{1.100064in}}%
\pgfpathlineto{\pgfqpoint{3.918182in}{1.169342in}}%
\pgfpathlineto{\pgfqpoint{4.322727in}{1.238416in}}%
\pgfpathlineto{\pgfqpoint{4.368182in}{1.225585in}}%
\pgfpathlineto{\pgfqpoint{4.468182in}{1.197092in}}%
\pgfpathlineto{\pgfqpoint{4.468182in}{1.197092in}}%
\pgfusepath{stroke}%
\end{pgfscope}%
\begin{pgfscope}%
\pgfpathrectangle{\pgfqpoint{0.750000in}{0.571935in}}{\pgfqpoint{4.650000in}{0.836130in}}%
\pgfusepath{clip}%
\pgfsetbuttcap%
\pgfsetroundjoin%
\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
\pgfsetfillcolor{currentfill}%
\pgfsetlinewidth{1.003750pt}%
\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
\pgfsetstrokecolor{currentstroke}%
\pgfsetdash{}{0pt}%
\pgfsys@defobject{currentmarker}{\pgfqpoint{4.107300in}{1.100359in}}{\pgfqpoint{4.594000in}{1.370059in}}{%
\pgfpathmoveto{\pgfqpoint{4.594000in}{1.115859in}}%
\pgfpathlineto{\pgfqpoint{4.594000in}{1.100359in}}%
\pgfpathlineto{\pgfqpoint{4.107300in}{1.100359in}}%
\pgfpathlineto{\pgfqpoint{4.107300in}{1.193359in}}%
\pgfpathlineto{\pgfqpoint{4.183250in}{1.370059in}}%
\pgfpathlineto{\pgfqpoint{4.470000in}{1.370059in}}%
\pgfpathlineto{\pgfqpoint{4.470000in}{1.193359in}}%
\pgfpathlineto{\pgfqpoint{4.594000in}{1.193359in}}%
\pgfpathlineto{\pgfqpoint{4.594000in}{1.115859in}}%
\pgfpathlineto{\pgfqpoint{4.594000in}{1.115859in}}%
\pgfpathlineto{\pgfqpoint{4.470000in}{1.115859in}}%
\pgfpathlineto{\pgfqpoint{4.470000in}{1.115859in}}%
\pgfpathlineto{\pgfqpoint{4.183250in}{1.115859in}}%
\pgfpathlineto{\pgfqpoint{4.107300in}{1.115859in}}%
\pgfpathlineto{\pgfqpoint{4.107300in}{1.115859in}}%
\pgfpathlineto{\pgfqpoint{4.594000in}{1.115859in}}%
\pgfpathlineto{\pgfqpoint{4.594000in}{1.115859in}}%
\pgfpathclose%
\pgfusepath{stroke,fill}%
}%
\begin{pgfscope}%
\pgfsys@transformshift{0.000000in}{0.000000in}%
\pgfsys@useobject{currentmarker}{}%
\end{pgfscope}%
\end{pgfscope}%
\begin{pgfscope}%
\pgfpathrectangle{\pgfqpoint{0.750000in}{0.571935in}}{\pgfqpoint{4.650000in}{0.836130in}}%
\pgfusepath{clip}%
\pgfsetbuttcap%
\pgfsetroundjoin%
\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
\pgfsetfillcolor{currentfill}%
\pgfsetlinewidth{1.003750pt}%
\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
\pgfsetstrokecolor{currentstroke}%
\pgfsetdash{}{0pt}%
\pgfsys@defobject{currentmarker}{\pgfqpoint{3.952300in}{1.100359in}}{\pgfqpoint{4.183250in}{1.263109in}}{%
\pgfpathmoveto{\pgfqpoint{4.183250in}{1.115859in}}%
\pgfpathlineto{\pgfqpoint{4.183250in}{1.100359in}}%
\pgfpathlineto{\pgfqpoint{4.183250in}{1.263109in}}%
\pgfpathlineto{\pgfqpoint{3.952300in}{1.263109in}}%
\pgfpathlineto{\pgfqpoint{3.955400in}{1.100359in}}%
\pgfpathlineto{\pgfqpoint{3.955400in}{1.115859in}}%
\pgfpathlineto{\pgfqpoint{3.955400in}{1.115859in}}%
\pgfpathlineto{\pgfqpoint{3.952300in}{1.115859in}}%
\pgfpathlineto{\pgfqpoint{4.183250in}{1.115859in}}%
\pgfpathlineto{\pgfqpoint{4.183250in}{1.115859in}}%
\pgfpathlineto{\pgfqpoint{4.183250in}{1.115859in}}%
\pgfpathclose%
\pgfusepath{stroke,fill}%
}%
\begin{pgfscope}%
\pgfsys@transformshift{0.000000in}{0.000000in}%
\pgfsys@useobject{currentmarker}{}%
\end{pgfscope}%
\end{pgfscope}%
\end{pgfpicture}%
\makeatother%
\endgroup%

2096
report/fig/map.pgf Normal file
View file

File diff suppressed because it is too large Load diff

8
report/library.bib
View file

@ -68,3 +68,11 @@
year={2011},
publisher={Elsevier}
}
@misc{shomsjl,
author="SHOM",
title="MNT topo-bathymétrique côtier de la baie de Saint-Jean-de-Luz et de ses abords a 20m (Projet TANDEM).",
year="2016",
doi={10.17183/MNT_COTIER_BAIE_SJL_TANDEM_20m_WGS84},
url={http://dx.doi.org/10.17183/MNT_COTIER_BAIE_SJL_TANDEM_20m_WGS84},
}

94
report/main.tex
View file

@ -89,6 +89,100 @@ following computations, as it represents the expected porosity of such a
block armour.
\section{Methods}
\subsection{Model}
In this project, we will model the transformation of a storm wave over the
Artha breakwater using the olaFlow (\cite{olaFlow}) model in a two-dimensionnal
domain. This model has several features that will be important for this study.
It provides powerful wave-generation and wave absorption capabilities, as well
as the ability to study two-phase flow through porous media.
The olaFlow model is based on VARANS equations\footnote{Volume-Averaged
Reynolds-Averaged Navier-Stokes equations}. This model is based on a
finite-volume approach, and provides multiple volume-averaging methods for
turbulence: the $k-\varepsilon$ model and the $k-\omega$ sst model. The
$k-\omega$ sst model should provide better results in situations where strong
pressure gradients are present, at the cost of computing power.
For the purposes of this initial sensibility study, the $k-\omega$ model will
be used.
\subsection{Domain}
The studied domain will be a two-dimensionnal vertical slice going through the
Artha breakwater. In order to provide accurate results while keeping
computation times acceptable, a domain length of \SI{150}{\m} was chosen, with
a length of \SI{120}{\m} towards the offshore and \SI{30}{\m} towards the
inside of the Saint-Jean-de-Luz bay, as shown in \autoref{fig:map}.
\begin{figure}
\centering
\input{fig/map.pgf}
\caption{Studied domain.}\label{fig:map}
\end{figure}
The bathymetry was generated using bathymetric data from the SHOM
(\cite{shomsjl}). Although the density of points is fairly low in this data,
it should be precise enough for the purposes of this project.
In addition to this data, the geometry of the superstructure was taken from
\cite{amir}, and the size of the porous armor layer was inspired from
\cite{poncet2021characterization}. The necessary stl files that are used by
snappyHexMesh for the solid boundaries and olaFlow for the porosity
configuration were generated using a custom python script, and the resulting
case is plotted in \autoref{fig:conf}.
\begin{figure}
\centering
\input{fig/bathy.pgf}
\caption{Studied configuration (bathymetry and porosity).}\label{fig:conf}
\end{figure}
\subsection{Mesh}
In order to provide accurate results with an acceptable computation time, a
mesh with \SI{1}{\m} cells was generated on the domain. It seems like olaFlow
cannot use variable mesh sizing, which meant that the mesh was still fairly
coarse near the edges of the domain.
The boundary conditions were set to a wave generator on the offshore boundary,
and a wave absorption boundary on the bay side. The bottom and the caisson were
set to wall boundaries, and the top side of the domain was set to an
atmospheric boundary.
\subsection{Model setup}
In an attempt to model the event of February 2017 in Saint-Jean-de-Luz, the
water level was set to \SI{5}{\m}. The inbound wave on the offshore side of
the domain was set as a solitary Boussinesq wave, with a wave height
$H=\SI{7.5}{\m}$. The wave equation is the following:
\begin{equation}
\eta=H\left[\sech\sqrt{\frac 34\frac Hh\frac{x-ct}h}\right]^2
\end{equation}
\subsection{Porosity setup}
The goal of the study is to find out the influence of the porosity parameters
on the model results. Porosity in the olaFlow model is goverened by five
parameters: a, b, c are tuning parameters that represent friction inside
the porous material, D50 is the mean nominal diameter of blocks, and porosity.
In this study, we will focus on the D50 and porosity parameters, as a, b and c
should be tuned according to experimental data. The friction parameters will be
set to the default from the breakwater example in the olaFlow model.
Four cases will be run, with all combinations of the parameters in
\autoref{tab:params}. The D50 parameters is based on the smallest and largest
edge size of the blocks that make up the breakwater armour. The porosity
parameters are based on the work of \cite{poncet2021characterization}, with
\num{0.40} being the value that he used for the numerical study, and \num{0.25}
being the value that yielded the lowest error in the model calibration.
\begin{table}
\centering
\begin{tabular}{lcc}
\toprule
\bfseries Parameters & & \\
\midrule
D50 & \SI{4}{\m} & \SI{2}{\m} \\
Porosity & \num{0.40} & \num{0.25} \\
\bottomrule
\end{tabular}
\caption{Parameter values.}\label{tab:params}
\end{table}
\section{Results}