@article {MolaHeltaiDeSimone2017,
	title = {Wet and Dry Transom Stern Treatment for Unsteady and Nonlinear Potential Flow Model for Naval Hydrodynamics Simulations},
	journal = {Journal of Ship Research},
	volume = {61},
	number = {1},
	year = {2017},
	pages = {1{\textendash}14},
	abstract = {<p>We present a model for the fast evaluation of the total drag of ship hulls operating in both wet and dry transom stern conditions, in calm or wavy water, based on the combination of an unsteady semi-Lagrangian potential flow formulation with fully nonlinear free-surface treatment, experimental correlations, and simplified viscous drag modeling. The implementation is entirely based on open source libraries. The spatial discretization is solved using a streamline upwind Petrov-Galerkin stabilization of an iso-parametric, collocation based, boundary element method, implemented using the open source library deal.II. The resulting nonlinear differential-algebraic system is integrated in time using implicit backward differentiation formulas, implemented in the open source library SUNDIALS. The Open CASCADE library is used to interface the model directly with computer-aided design data structures. The model accounts automatically for hulls with a transom stern, both in wet and dry regimes, by using a specific treatment of the free-surface nodes on the stern edge that automatically detects when the hull advances at low speeds. In this case, the transom stern is partially immersed, and a pressure patch is applied on the water surface detaching from the transom stern, to recover the gravity effect of the recirculating water on the underlying irrotational flow domain. The parameters of the model used to impose the pressure patch are approximated from experimental relations found in the literature. The test cases considered are those of the U.S. Navy Combatant DTMB-5415 and the National Physical Laboratory hull. Comparisons with experimental data on quasi-steady test cases for both water elevation and total hull drag are presented and discussed. The quality of the results obtained on quasi-steady simulations suggests that this model can represent a promising alternative to current unsteady solvers for simulations with Froude numbers below 0.35.</p>},
	doi = {https://doi.org/10.5957/JOSR.61.1.160016},
	author = {Andrea Mola and Luca Heltai and Antonio DeSimone}
}
@article {2005,
	title = {Wetting of rough surfaces: a homogenization approach},
	journal = {Proc. R. Soc. Lon. Ser. A 461 (2005) 79-97},
	number = {SISSA;75/2004/M},
	year = {2005},
	abstract = {The contact angle of a drop in equilibrium on a solid is strongly affected by the roughness of the surface on which it rests. We study the roughness-induced enhancement of the hydrophobic or hydrophilic properties of a solid surface through homogenization theory. By relying on a variational formulation of the problem, we show that the macroscopic contact angle is associated with the solution of two cell problems, giving the minimal energy per unit macroscopic area for a transition layer between the rough solid surface and a liquid or vapor phase. Our results are valid for both chemically heterogeneous and homogeneous surfaces. In the latter case, a very transparent structure emerges from the variational\\napproach: the classical laws of Wenzel and Cassie-Baxter give bounds for the optimal energy, and configurations of minimal energy are those leading to the smallest macroscopic contact angle in the hydrophobic case, to the largest one in the hydrophilic case.},
	doi = {10.1098/rspa.2004.1364},
	url = {http://hdl.handle.net/1963/2253},
	author = {Antonio DeSimone and Giovanni Alberti}
}
