2 research outputs found
Spaceātime NURBSāenhanced finite elements for freeāsurface flows in 2D
The accuracy of numerical simulations of freeāsurface 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 NURBSāenhanced finite element method (NEFEM), recently proposed by Sevilla et al. The current paper discusses the extension of the spatial NEFEM to spaceātime methods and investigates the application of spaceātime NURBSāenhanced elements to freeāsurface 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 spaceātime NEFEM to account for both pressure discontinuities and surface tension effects and compute smooth freeāsurface forms. For these examples, the advantages of the NEFEM compared with the classical FEM are shown.