Laura Battaglia

Simulation of free-surface flows by a finite element interface capturing technique

Transient free-surface (FS) flows are numerically simulated by a finite element interface capturing method based on a level set approach. The methodology consists of the solution of two-fluid viscous incompressible flows for a single domain, where the liquid phase is identified by the positive values of the level set function, the gaseous phase by negative ones, and the FS by the zero level set. The numerical solution at each time step is performed in three stages: (i) a two-fluid Navier–Stokes stage, (ii) an advection stage for the transport of the level set function and (iii) a bounded reinitialisation with continuous penalisation stage for keeping smoothness of the level set function. The proposed procedure, and particularly the renormalisation stage, is evaluated in three typical two- and three-dimensional problems.

A semi-analytical computation of the Kelvin kernel for potential flows with a free surface

A semi-analytical computation of the three dimensional Green function for seakeeping flow problems is proposed. A potential flow model is assumed with an harmonic dependence on time and a linearized free surface boundary condition. The multiplicative Green function is expressed as the product of a time part and a spatial one. The spatial part is known as the Kelvin kernel, which is the sum of two Rankine sources and a wave-like kernel, being the last one written using the Haskind-Havelock representation. Numerical efficiency is improved by an analytical integration of the two Rankine kernels and the use of a singularity subtractive technique for the Haskind-Havelock integral, where a globally adaptive quadrature is performed for the regular part and an analytic integration is used for the singular one. The proposed computation is employed in a low order panel method with flat triangular elements. As a numerical example, an oscillating floating unit hemisphere in heave and surge modes is considered, where analytical and semi-analytical solutions are taken as a reference.