Abstract

In this paper, we present a finite element model for free surface flows on fixed meshes. The main novelty of the approach, compared with typical fixed mesh finite element models for such flows, is that we take advantage of the particularities of free surface flow, instead of considering it a particular case of two‐phase flow. The fact that a given free surface implies a known boundary condition on the interface, allows us to solve the Navier–Stokes equations on the fluid domain uncoupled from the solution on the rest of the finite element mesh. This, together with the use of enhanced integration allows us to model low Froude number flows accurately, something that is not possible with typical two‐phase flow models applied to free surface flow.

Abstract

The simulation of low Froude number mould filling problems on fixed meshes presents significant difficulties. As the Froude number decreases, the coupling between the position of the interface and the resulting flow field increases. The usual two‐phase flow model provides poor results for such flow. In order to overcome the difficulties, a free surface model that applies boundary conditions at the interface accurately is used. Moreover, the use of wall laws on curved boundaries also fails in the case of low Froude number flows. To solve this second problem, we combine wall laws with ‘do nothing’ boundary conditions. A special feature of our approach is that ‘do nothing’ boundary conditions are only applied in the normal direction. These two key ingredients together with the Level Set method allow us to simulate three‐dimensional mould filling problems borrowed directly from the foundry.