Interface-Tracking Free-Surface Flows in Open Domains

Abstract

An arbitrary Lagrangian-Eulerian method is used for solving incompressible free-surface flows with the finite element method, assuming that the fluid is viscous and Newtonian. The flow is represented over a domain with a single fluid, where one of the frontiers is a free surface. The computational scheme consists of three main stages: (i) the resolution of the Navier-Stokes equations for the fluid state, with equal order elements for velocity and pressure, stabilized with the streamline-upwind/Petrov-Galerkin and the pressure-stabilizing/Petrov-Galerkin strategies; (ii) the determination of the free surface displacements, as a function of the velocities from the Navier-Stokes stage; (iii) the mesh update procedure, which is performed by a pseudo-elastic problem solved with the free-surface nodal movements as imposed displacements. The main attention here is focused on open domains, where artificial boundaries are proposed in order to bound the numerical problem. The numerical examples consist of free-surface flows with artificial contours, and the results are compared with reference solutions.