A computational framework for free surface fluid flows accounting for surface tension

This work is concerned with the simulation of incompressible Newtonian fluid flow problems with free surfaces in the presence of surface tension. The computational framework presented is based on the stabilised velocity–pressure finite element method. The movement and deformation of the computational domain are accounted for by employing the arbitrary Lagrangian–Eulerian (ALE) description of the fluid kinematics. The numerical model is extended to incorporate surface tension effects. A novel partitioned solution procedure is developed based on the Newton–Raphson methodology which incorporates full linearisation of the overall incremental problem. Several numerical examples are provided to demonstrate the efficiency of the methodology.