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

Author (s): Stavrev, A., Knechtges, P., Elgeti, S., and Huerta A.
Journal: International Journal for Numerical Methods in Fluids

Volume: 81, Issue 7
Pages: 426 – 450
Date: 2016

The 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 to the classical FEM are shown.



        Author = {Atanas Stavrev and Philipp Knechtges and Stefanie Elgeti and Antonio Huerta},
        Title = {Space-time {NURBS}-enhanced finite elements for free-surface flows in 2{D}},
        Fjournal = {International Journal for Numerical Methods in Fluids},
        Journal = {Int. J. Numer. Methods Fluids},
        Volume = {81},
        Number = {7},
        Pages = {426--450},
        Year = {2016},
        Doi = {10.1002/fld.4189},