On the calculation of normals in free-surface flow problems

The use of boundary-conforming finite element methods is considered for the solution of surface-tension-dominated free-surface flow problems in three dimensions. This class of method is based upon the use of a moving mesh whose velocity is driven by the motion of the free surface, which is in turn determined via a kinematic boundary condition for the normal velocity. The significance of the method used to compute the normal direction at the finite element node points for a C0 piecewise-polynomial free surface is investigated.

In particular, it is demonstrated that the concept of mass-consistent normals on an isoparametric quadratic tetrahedral mesh is flawed. In this case an alternative, purely geometric, normal is shown to lead to a far more robust numerical algorithm.