Stabilized Free Surface Flows.

Abstract

In this work, numerical simulations of free surface flows of incompressible and viscous
fluids are performed by a finite element computation. As presented in previous works, the free surface
movement is followed by a mesh-movement technique (see Battaglia et al, Mec´anica Computacional, Vol
XXIV, pp. 105-116, Buenos Aires, Argentina, Nov. 2005), but because of the fully explicit character of
the free surface update equation a smoothing process was used to avoid numerical instabilities. Regarding
that the kinematic boundary condition at the interface can be described as a transport-like equation,
different authors suggested consistent stabilized finite-element formulations for the free surface, such
as streamline upwind/P´etrov-Galerkin (SUPG) (Soula¨ımani et al, Comp. Meth. Appl. Mech. Engrg.,
Vol. 86(3), 1991; G¨uler et al, Computational Mechanics, vol. 23, pp. 117-123, 1999) or Galerkin/Least-
Squares (GLS) (Behr et al, Comp. Meth. Appl. Mech. Engrg., Vol. 191(47-48), pp. 5467-5483, Nov.
2002). In this work, a numerical stabilization with this aim is performed as a part of the multi-physics
finite element code PETSc-FEM (http://www.cimec.org.ar/petscfem/). Numerical examples are shown.