Arbitrary Lagrangian–Eulerian and free surface methods in fluid mechanics Original Research Article

A computational procedure is developed to solve problems of viscous incompressible flows under large free surface motions. The arbitrary Lagrangian–Eulerian (ALE) method is used to move the free surface nodes as well as the internal nodes. The coupling of the mesh motion equations and the fluid equations is essentially done through the free surface boundary conditions. An elastic model with free surface boundary conditions is used to model the mesh motion. The boundary condition at the free surface is deduced from the fact that no fluid particle can cross the free surface. The fluid problem is solved using a Galerkin/least-square (GLS) finite element formulation.