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

作者：Stavrev A^*; Knechtges P; Elgeti S; Huerta A

来源：International Journal for Numerical Methods in Fluids, 2016, 81(7): 426-450.

DOI：10.1002/fld.4189

• free-surface flows
• space-time NURBS-enhanced finite element method
• surface tracking
• kinematic conditions
• mass conservation
• boundary conforming mesh

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 with the classical FEM are shown.

• 出版日期2016-7-10