Biblio: VOF models
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@ -202,30 +202,110 @@ representation of the fluid.
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\cite{altomare2017long}
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\cite{wen2018non}
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\subsection{VARANS models}
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\subsection{VOF models}
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\cite{van1995wave,troch1999development}
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\subsubsection{Introduction}
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COBRAS \parencite{liu1999numerical}: spatially averaged RANS
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with $k-\varepsilon$ turbulence model. Drag forces modeled by empirical linear
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and non-linear friction terms; \cite{hsu2002numerical}: introduced VARANS in
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order to account for small scale turbulence inside the porous media.
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->
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COBRAS-UC/IH2VOF \parencite{losada2008numerical,lara2008wave}: VOF VARANS (2D);
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refactor of COBRAS code, with improved wave generation, improvement of input
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and output data.
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->
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IH3VOF \parencite{del2011three}: 3D VOF VARANS, updated porous media equations,
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optimization of accuracy vs computation requirements, specific boundary
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conditions, validation. Adding SST model.
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->
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IHFOAM/olaFlow \parencite{higuera2015application}: Rederivation of
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\cite{del2011three}, add time-varying porosity; Improvement to wave generation
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and absorption; implementation in OpenFOAM; extensive validation; application
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to real coastal structures.
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Contrary to SPH models, the volume of fluid (VOF) method relies on a Eulerian
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representation of the fluid \parencite{hirt1981volume}. This method uses a
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marker function, the value of which represents the fraction of fluid in a cell.
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\cite{vieira2021novel}: Use of artificial neural networks to determine porosity
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parameter for VOF VARANS model.
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\subsubsection{2D models}
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Using the VOF method along with Navier-Stokes equations, several models have
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been developed in order to model fluid dynamics around porous structures.
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\textcite{van1995wave} first implemented 2D-V incompressible Navier-Stokes
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equations using the VOF method while accounting for porous media. The results
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of the numerical model were validated with analytical solutions for simple
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cases, as well as physical model tests. The model yielded acceptable results,
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but the representation of turbulence and air-extrusion still required
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improvement.
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\textcite{troch1999development} developed the VOFbreak\textsuperscript{2} model
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in order to provide improvements. The Forchheimer theory
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\parencite{burcharth1995one} is used in order to model the behavior of the flow
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inside porous media. The hydraulic gradient generated in porous media is
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decomposed as a linear term, a quadratic term, and an inertia term. Those terms
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are ponderated by three coefficients that need to be calibrated. Several
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attempts have been made to obtain analytical formulas for those
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\parencite{burcharth1995one,van1995wave}, but no universal result has been
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provided. \textcite{vieira2021novel} additionnaly proposed using artificial
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neural networks in order to calibrate those values, which are generally
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calibrated using experimental results.
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Parallely, \textcite{liu1999numerical} created a new model (COBRAS) that used
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the VOF method. The model is based on the combination of Reynolds averaged
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Navier-Stokes (RANS) equations and a $k-\varepsilon$ turbulence model. The
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porous media is modelled similarly to \textcite{troch1999development}. The
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offered results were improved compared to earlier models as more a more
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accurate consideration of turbulence outside porous media was added. This model
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was further improved by \textcite{hsu2002numerical} in order to account for
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small scale turbulence inside the porous media thanks to volume averaged RANS
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(VARANS) equations.
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The COBRAS model was then reworked by
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\textcite{losada2008numerical,lara2008wave} to add improvements to wave
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generation and usability. The main difference between this new code (COBRAS-UC)
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and COBRAS is the addition of irregular waves generation. The code was also
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optimized to reduce the number of iterations. The improvements allowed for
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longer simulations to be computed. The predictions for free surface elevation
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and pressure in front of a porous breakwater were accurate, but improvements
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were still needed, in particular considering computation time.
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\subsubsection{3D models}
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The combination of VARANS equations and the VOF method was then brought to 3D
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domains by \textcite{del2011three} in IH3VOF. Specific boundary conditions were
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also added for several wave theories. Additionnaly, an improved turbulence
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model was used ($\omega$-SST model, \cite{menter1994two}), which provides
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strongly improved results in zones where strong pressure gradients appear.
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Strong agreement between IH3VOF and experimental results was obtained, but the
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need for accurate boundary conditions limited the applicability of the model.
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\textcite{higuera2015application} reworked the equations from
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\textcite{del2011three} as discrepancies were observed with earlier literature
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and added several improvements to the model. Notably, time-varying porosity was
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added in order to account for eventual sediment displacement. New boundary
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conditions were added, with static and dynamic boundary wave generators as well
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as passive and acive wave absorption being implemented. The resulting model
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(IHFOAM/olaFlow, \cite{olaFlow}) was implemented in the OpenFOAM toolbox.
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\subsubsection{Conclusion}
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VOF models have been developped to provide accurate results for the study of
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wave impact on porous structures. The validation results from
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\textcite{higuera2015application} show the capabilities of such models in
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accurately representing rubble-mound breakwaters subject to irregular
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three-dimensional wave fields.
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Nonetheless, the representation of porosity in those models is still mainly
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based on experimental calibration, particularly for the inertia term of
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porosity induced friction.
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%\paragraph{Notes}
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%
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%\cite{van1995wave,troch1999development}
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%
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%COBRAS \parencite{liu1999numerical}: spatially averaged RANS
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%with $k-\varepsilon$ turbulence model. Drag forces modeled by empirical linear
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%and non-linear friction terms; \cite{hsu2002numerical}: introduced VARANS in
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%order to account for small scale turbulence inside the porous media.
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%->
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%COBRAS-UC/IH2VOF \parencite{losada2008numerical,lara2008wave}: VOF VARANS (2D);
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%refactor of COBRAS code, with improved wave generation, improvement of input
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%and output data.
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%->
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%IH3VOF \parencite{del2011three}: 3D VOF VARANS, updated porous media equations,
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%optimization of accuracy vs computation requirements, specific boundary
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%conditions, validation. Adding SST model.
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%->
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%IHFOAM/olaFlow \parencite{higuera2015application}: Rederivation of
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%\cite{del2011three}, add time-varying porosity; Improvement to wave generation
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%and absorption; implementation in OpenFOAM; extensive validation; application
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%to real coastal structures.
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%
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%\cite{vieira2021novel}: Use of artificial neural networks to determine porosity
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%parameter for VOF VARANS model.
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\subsection{Other}
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@ -915,3 +915,42 @@
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publisher={Molecular Diversity Preservation International}
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}
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@article{hirt1981volume,
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title={Volume of fluid (VOF) method for the dynamics of free boundaries},
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author={Hirt, Cyril W and Nichols, Billy D},
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journal={Journal of computational physics},
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volume={39},
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number={1},
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pages={201--225},
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year={1981},
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publisher={Elsevier}
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}
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@incollection{van1993numerical,
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title={Numerical simulation of wave motion on and in coastal structures},
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author={Van der Meer, JW and Petit, HAH and Van den Bosch, P and Klopman, G and Broekens, RD},
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booktitle={Coastal Engineering 1992},
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pages={1772--1784},
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year={1993}
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}
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@article{burcharth1995one,
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title={On the one-dimensional steady and unsteady porous flow equations},
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author={Burcharth, HF and Andersen, OK},
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journal={Coastal engineering},
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volume={24},
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number={3-4},
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pages={233--257},
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year={1995},
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publisher={Elsevier}
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}
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@article{menter1994two,
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title={Two-Equation Eddy-Viscosity Turbulence Models for Engineering Applications},
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author={Menter, FR},
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journal={AIA A JOURNAL},
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volume={32},
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number={8},
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year={1994}
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}
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@ -4,7 +4,6 @@
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\usepackage[
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backend=biber,
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sorting=ynt,
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style=iso-authoryear,
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sorting=nyt,
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]{biblatex}
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