Biblio: VOF models

biblio/chapters/literature.tex

@@ -202,30 +202,110 @@ representation of the fluid.
 \cite{altomare2017long}
 \cite{wen2018non}
 
-\subsection{VARANS models}
+\subsection{VOF models}
 
-\cite{van1995wave,troch1999development}
+\subsubsection{Introduction}
 
-COBRAS \parencite{liu1999numerical}: spatially averaged RANS
-with $k-\varepsilon$ turbulence model. Drag forces modeled by empirical linear
-and non-linear friction terms; \cite{hsu2002numerical}: introduced VARANS in
-order to account for small scale turbulence inside the porous media.
-->
-COBRAS-UC/IH2VOF \parencite{losada2008numerical,lara2008wave}: VOF VARANS (2D);
-refactor of COBRAS code, with improved wave generation, improvement of input
-and output data.
-->
-IH3VOF \parencite{del2011three}: 3D VOF VARANS, updated porous media equations,
-optimization of accuracy vs computation requirements, specific boundary
-conditions, validation. Adding SST model.
-->
-IHFOAM/olaFlow \parencite{higuera2015application}: Rederivation of
-\cite{del2011three}, add time-varying porosity; Improvement to wave generation
-and absorption; implementation in OpenFOAM; extensive validation; application
-to real coastal structures.
+Contrary to SPH models, the volume of fluid (VOF) method relies on a Eulerian
+representation of the fluid \parencite{hirt1981volume}. This method uses a
+marker function, the value of which represents the fraction of fluid in a cell.
 
-\cite{vieira2021novel}: Use of artificial neural networks to determine porosity
-parameter for VOF VARANS model.
+\subsubsection{2D models}
+
+Using the VOF method along with Navier-Stokes equations, several models have
+been developed in order to model fluid dynamics around porous structures.
+\textcite{van1995wave} first implemented 2D-V incompressible Navier-Stokes
+equations using the VOF method while accounting for porous media. The results
+of the numerical model were validated with analytical solutions for simple
+cases, as well as physical model tests. The model yielded acceptable results,
+but the representation of turbulence and air-extrusion still required
+improvement.
+
+\textcite{troch1999development} developed the VOFbreak\textsuperscript{2} model
+in order to provide improvements. The Forchheimer theory
+\parencite{burcharth1995one} is used in order to model the behavior of the flow
+inside porous media. The hydraulic gradient generated in porous media is
+decomposed as a linear term, a quadratic term, and an inertia term. Those terms
+are ponderated by three coefficients that need to be calibrated. Several
+attempts have been made to obtain analytical formulas for those
+\parencite{burcharth1995one,van1995wave}, but no universal result has been
+provided. \textcite{vieira2021novel} additionnaly proposed using artificial
+neural networks in order to calibrate those values, which are generally
+calibrated using experimental results.
+
+Parallely, \textcite{liu1999numerical} created a new model (COBRAS) that used
+the VOF method. The model is based on the combination of Reynolds averaged
+Navier-Stokes (RANS) equations and a $k-\varepsilon$ turbulence model. The
+porous media is modelled similarly to \textcite{troch1999development}. The
+offered results were improved compared to earlier models as more a more
+accurate consideration of turbulence outside porous media was added. This model
+was further improved by \textcite{hsu2002numerical} in order to account for
+small scale turbulence inside the porous media thanks to volume averaged RANS
+(VARANS) equations.
+
+The COBRAS model was then reworked by
+\textcite{losada2008numerical,lara2008wave} to add improvements to wave
+generation and usability. The main difference between this new code (COBRAS-UC)
+and COBRAS is the addition of irregular waves generation. The code was also
+optimized to reduce the number of iterations. The improvements allowed for
+longer simulations to be computed. The predictions for free surface elevation
+and pressure in front of a porous breakwater were accurate, but improvements
+were still needed, in particular considering computation time.
+
+\subsubsection{3D models}
+
+The combination of VARANS equations and the VOF method was then brought to 3D
+domains by \textcite{del2011three} in IH3VOF. Specific boundary conditions were
+also added for several wave theories. Additionnaly, an improved turbulence
+model was used ($\omega$-SST model, \cite{menter1994two}), which provides
+strongly improved results in zones where strong pressure gradients appear.
+Strong agreement between IH3VOF and experimental results was obtained, but the
+need for accurate boundary conditions limited the applicability of the model.
+
+\textcite{higuera2015application} reworked the equations from
+\textcite{del2011three} as discrepancies were observed with earlier literature
+and added several improvements to the model. Notably, time-varying porosity was
+added in order to account for eventual sediment displacement. New boundary
+conditions were added, with static and dynamic boundary wave generators as well
+as passive and acive wave absorption being implemented. The resulting model
+(IHFOAM/olaFlow, \cite{olaFlow}) was implemented in the OpenFOAM toolbox.
+
+\subsubsection{Conclusion}
+
+VOF models have been developped to provide accurate results for the study of
+wave impact on porous structures. The validation results from
+\textcite{higuera2015application} show the capabilities of such models in
+accurately representing rubble-mound breakwaters subject to irregular
+three-dimensional wave fields.
+
+Nonetheless, the representation of porosity in those models is still mainly
+based on experimental calibration, particularly for the inertia term of
+porosity induced friction.
+
+%\paragraph{Notes}
+%
+%\cite{van1995wave,troch1999development}
+%
+%COBRAS \parencite{liu1999numerical}: spatially averaged RANS
+%with $k-\varepsilon$ turbulence model. Drag forces modeled by empirical linear
+%and non-linear friction terms; \cite{hsu2002numerical}: introduced VARANS in
+%order to account for small scale turbulence inside the porous media.
+%->
+%COBRAS-UC/IH2VOF \parencite{losada2008numerical,lara2008wave}: VOF VARANS (2D);
+%refactor of COBRAS code, with improved wave generation, improvement of input
+%and output data.
+%->
+%IH3VOF \parencite{del2011three}: 3D VOF VARANS, updated porous media equations,
+%optimization of accuracy vs computation requirements, specific boundary
+%conditions, validation. Adding SST model.
+%->
+%IHFOAM/olaFlow \parencite{higuera2015application}: Rederivation of
+%\cite{del2011three}, add time-varying porosity; Improvement to wave generation
+%and absorption; implementation in OpenFOAM; extensive validation; application
+%to real coastal structures.
+%
+%\cite{vieira2021novel}: Use of artificial neural networks to determine porosity
+%parameter for VOF VARANS model.
 
 \subsection{Other}
 

biblio/library.bib

@@ -915,3 +915,42 @@
   publisher={Molecular Diversity Preservation International}
 }
 
+@article{hirt1981volume,
+  title={Volume of fluid (VOF) method for the dynamics of free boundaries},
+  author={Hirt, Cyril W and Nichols, Billy D},
+  journal={Journal of computational physics},
+  volume={39},
+  number={1},
+  pages={201--225},
+  year={1981},
+  publisher={Elsevier}
+}
+
+@incollection{van1993numerical,
+  title={Numerical simulation of wave motion on and in coastal structures},
+  author={Van der Meer, JW and Petit, HAH and Van den Bosch, P and Klopman, G and Broekens, RD},
+  booktitle={Coastal Engineering 1992},
+  pages={1772--1784},
+  year={1993}
+}
+
+@article{burcharth1995one,
+  title={On the one-dimensional steady and unsteady porous flow equations},
+  author={Burcharth, HF and Andersen, OK},
+  journal={Coastal engineering},
+  volume={24},
+  number={3-4},
+  pages={233--257},
+  year={1995},
+  publisher={Elsevier}
+}
+
+@article{menter1994two,
+  title={Two-Equation Eddy-Viscosity Turbulence Models for Engineering Applications},
+  author={Menter, FR},
+  journal={AIA A JOURNAL},
+  volume={32},
+  number={8},
+  year={1994}
+}
+

biblio/main.tex

@@ -4,7 +4,6 @@
 
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