Space-time NURBS-enhanced finite elements for free-surface flows in 2D

This is the accepted version of the following article: Stavrev, A., Knechtges, P., Elgeti, S., and Huerta, A. (2016) Space-time NURBS-enhanced finite elements for free-surface flows in 2D., Int. J. Numer. Meth. Fluids, doi: 10.1002/fld.4189, which has been published in final form at http://onlinelibrary.wiley.com/doi/10.1002/fld.4189/abstractThe accuracy of numerical simulations of free-surface flows depends strongly on the computation of geometric quantities like normal vectors and curvatures. This geometrical information is additional to the actual degrees of freedom and usually requires a much finer discretization of the computational domain than the flow solution itself. Therefore, the utilization of a numerical method, which uses standard functions to discretize the unknown function in combination with an enhanced geometry representation is a natural step to improve the simulation efficiency. An example of such method is the NURBS-enhanced finite element method (NEFEM), recently proposed by Sevilla et al. The current paper discusses the extension of the spatial NEFEM to space-time methods and investigates the application of space-time NURBS-enhanced elements to free-surface flows. Derived is also a kinematic rule for the NURBS motion in time, which is able to preserve mass conservation over time. Numerical examples show the ability of the space-time NEFEM to account for both pressure discontinuities and surface tension effects and compute smooth free-surface forms. For these examples, the advantages of the NEFEM compared with the classical FEM are shown.Peer ReviewedPostprint (author's final draft