The extended finite element method applied to 3D free-surface flows

In fluid flow problems with free surfaces, discontinuities in the field variables can occur across the interface. Such non-smooth solution behavior causes great problems for standard finite element methods in combination with interface capturing techniques. An approach frequently applied to problems with discontinuous solutions is the extended finite element method (XFEM). The discontinuities across the interface can be appropriately accounted for by locally enriching the finite element approximation space. As the XFEMis based on the level set method, the possibility to deal with moving interfaces without topological restrictions is inherent. This work introduces a robust XFEM approach for free-surface flows. A special preconditioning technique is proposed which allows the usage of standard iterative solvers for the given XFEM problem. In order to increase the accuracy of the interface description and improve conservation of mass, an adaptive mesh refinement strategy is applied, where necessary. Furthermore, an extension of the mesh refinement approach is introduced which allows for the creation of efficient meshes involving curved boundaries. Very promising results for industrially relevant 3D free-surface flow simulations are presented.