From 70a4e4bb59a2a392af1940bbd8e2765b3f5c75a1 Mon Sep 17 00:00:00 2001 From: "Edgar P. Burkhart" Date: Mon, 31 Jan 2022 17:13:18 +0100 Subject: [PATCH] Report: Method --- report/cours.sty | 1 + report/fig/bathy.pgf | 684 ++++++++++++++ report/fig/map.pgf | 2096 ++++++++++++++++++++++++++++++++++++++++++ report/library.bib | 40 +- report/main.tex | 94 ++ 5 files changed, 2899 insertions(+), 16 deletions(-) create mode 100644 report/fig/bathy.pgf create mode 100644 report/fig/map.pgf diff --git a/report/cours.sty b/report/cours.sty index a351a29..8425ccf 100644 --- a/report/cours.sty +++ b/report/cours.sty @@ -115,6 +115,7 @@ \DeclareMathOperator\cond{cond} \DeclareMathOperator\erf{erf} \DeclareMathOperator\erfc{erfc} +\DeclareMathOperator\sech{sech} %%% Vecteurs et Matrices \renewcommand\u[1]{\underline{#1}} diff --git a/report/fig/bathy.pgf b/report/fig/bathy.pgf new file mode 100644 index 0000000..fb51ed5 --- /dev/null +++ b/report/fig/bathy.pgf @@ -0,0 +1,684 @@ +%% Creator: Matplotlib, PGF backend +%% +%% To include the figure in your LaTeX document, write +%% \input{.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{}{.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}% 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file mode 100644 index 0000000..3f1887b --- /dev/null +++ b/report/fig/map.pgf @@ -0,0 +1,2096 @@ +%% Creator: Matplotlib, PGF backend +%% +%% To include the figure in your LaTeX document, write +%% \input{.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{}{.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{6.400000in}{4.800000in}}% +\pgfusepath{use as bounding box, clip}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetmiterjoin% +\definecolor{currentfill}{rgb}{1.000000,1.000000,1.000000}% 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+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=5.298022in, y=4.171238in, left, base]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont 8}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=5.638333in,y=2.376000in,,top,rotate=90.000000]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont Altitude (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{5.016000in}{0.528000in}}% +\pgfpathlineto{\pgfqpoint{5.108400in}{0.528000in}}% +\pgfpathlineto{\pgfqpoint{5.200800in}{0.528000in}}% +\pgfpathlineto{\pgfqpoint{5.200800in}{4.224000in}}% +\pgfpathlineto{\pgfqpoint{5.108400in}{4.224000in}}% +\pgfpathlineto{\pgfqpoint{5.016000in}{4.224000in}}% +\pgfpathlineto{\pgfqpoint{5.016000in}{0.528000in}}% +\pgfpathclose% +\pgfusepath{stroke}% +\end{pgfscope}% +\end{pgfpicture}% +\makeatother% +\endgroup% diff --git a/report/library.bib b/report/library.bib index 446942a..7b205ce 100644 --- a/report/library.bib +++ b/report/library.bib @@ -48,23 +48,31 @@ } @article{nott2003waves, - title={Waves, coastal boulder deposits and the importance of the pre-transport setting}, - author={Nott, Jonathan}, - journal={Earth and Planetary Science Letters}, - volume={210}, - number={1-2}, - pages={269--276}, - year={2003}, - publisher={Elsevier} + title={Waves, coastal boulder deposits and the importance of the pre-transport setting}, + author={Nott, Jonathan}, + journal={Earth and Planetary Science Letters}, + volume={210}, + number={1-2}, + pages={269--276}, + year={2003}, + publisher={Elsevier} } @article{zijlema2011swash, - title={SWASH: An operational public domain code for simulating wave fields and rapidly varied flows in coastal waters}, - author={Zijlema, Marcel and Stelling, Guus and Smit, Pieter}, - journal={Coastal Engineering}, - volume={58}, - number={10}, - pages={992--1012}, - year={2011}, - publisher={Elsevier} + title={SWASH: An operational public domain code for simulating wave fields and rapidly varied flows in coastal waters}, + author={Zijlema, Marcel and Stelling, Guus and Smit, Pieter}, + journal={Coastal Engineering}, + volume={58}, + number={10}, + pages={992--1012}, + 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}, } diff --git a/report/main.tex b/report/main.tex index 9d2aaa0..75b9ba3 100644 --- a/report/main.tex +++ b/report/main.tex @@ -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}