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 C 0 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.