Robust control volume finite element methods for numerical wave tanks using extreme adaptive anisotropic meshes

Multiphase inertia-dominated flow simulations, and free surface flow models in particular, continue to this day to present many challenges in terms of accuracy and computational cost to industry and research communities. Numerical wave tanks and their use for studying wave-structure interactions are a good example. Finite element method (FEM) with anisotropic meshes combined with dynamic mesh algorithms has already shown the potential to significantly reduce the number of elements and simulation time with no accuracy loss. However, mesh anisotropy can lead to mesh quality-related instabilities. This article presents a very robust FEM approach based on a control volume discretization of the pressure field for inertia dominated flows, which can overcome the typically encountered mesh quality limitations associated with extremely anisotropic elements. Highly compressive methods for the water-air interface are used here. The combination of these methods is validated with multiphase free surface flow benchmark cases, showing very good agreement with experiments even for extremely anisotropic meshes, reducing by up to two orders of magnitude the required number of elements to obtain accurate solutions.