Space‐time NURBS‐enhanced finite elements for free‐surface flows in 2D
Space‐time NURBS‐enhanced finite elements for free‐surface flows in 2D
复制标题
时空 NURBS™ 二维自由表面流的增强有限元
DOI：
10.1002/fld.4189
复制
发表时间：
2016
影响因子：
1.8
通讯作者：
S. Huerta
中科院分区：
文献类型：
--
作者：
Stavrev;Knechtges;Elgeti;S. Huerta
自由表面流数值模拟的准确性在很大程度上取决于法向量和曲率等几何量的计算。该几何信息是实际自由度的附加信息，并且通常需要比流动解本身更精细的计算域离散化。因此，利用数值方法，使用标准函数结合增强的几何表示来离散化未知函数是提高模拟效率的自然步骤。这种方法的一个例子是 Sevillaet 等人最近提出的 NURBS 增强有限元法 (NEFEM)。本文讨论了空间 NEFEM 到时空方法的扩展，并研究了时空 NURBS 增强单元在自由表面流中的应用。导出的也是 NURBS 运动随时间变化的运动学规则，能够随时间保持质量守恒。数值示例表明时空 NEFEM 能够同时考虑压力不连续性和表面张力效应并计算平滑的自由表面形式。这些示例显示了 NEFEM 与经典 FEM 相比的优势。版权所有 © 2015 约翰·威利父子有限公司
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 Sevillaet 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. Copyright © 2015 John Wiley & Sons, Ltd.