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首页> 外文期刊>International Journal for Numerical Methods in Engineering >Fully implicit finite element method for the modeling of free surface flows with surface tension effect
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Fully implicit finite element method for the modeling of free surface flows with surface tension effect

机译：完全隐含的有限元方法，用于使用表面张力效果的自由表面流动

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摘要

A new approach based on the use of the Newton and level set methods allows to follow the motion of interfaces with surface tension immersed in an incompressible Newtonian fluid. Our method features the use of a high-order fully implicit time integration scheme that circumvents the stability issues related to the explicit discretization of the capillary force when capillary effects dominate. A strategy based on a consistent Newton-Raphson linearization is introduced, and performances are enhanced by using an exact Newton variant that guarantees a third-order convergence behavior without requiring second-order derivatives. The problem is approximated bymixed finite elements, while the anisotropic adaptivemesh refinements enable us to increase the computational accuracy. Numerical investigations of the convergence properties and comparisons with benchmark results provide evidence regarding the efficacy of the methodology. The robustness of the method is tested with respect to the standard explicit method, and stability is maintained for significantly larger time steps compared with those allowed by the stability condition. Copyright (C) 2016 John Wiley & Sons, Ltd.
机译：一种基于牛顿和级别设置方法的新方法允许沿着浸入不可压缩的牛顿液中的表面张力的界面的运动。我们的方法特征在于使用高阶完全隐含的时间集成方案，这些方案避免了毛细血管效应支配时毛细管力明确离散化相关的稳定性问题。介绍了一种基于一致的牛顿Raphson线性化的策略，使用精确的牛顿变体来增强性能，以保证三阶收敛行为而不需要二阶导数。问题是近似的有限元素近似，而各向异性适应性改进使我们能够提高计算精度。与基准结果的收敛性能和比较的数值研究提供了有关方法的功效的证据。与标准的明确方法测试了该方法的稳健性，与稳定条件允许的那些相比，保持稳定性的时间步长。版权所有（c）2016 John Wiley＆Sons，Ltd。

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