An arbitrary Lagrangian–Eulerian‐based finite element strategy for modeling incompressible two‐phase flows,International Journal for Numerical Methods in Fluids

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An arbitrary Lagrangian–Eulerian‐based finite element strategy for modeling incompressible two‐phase flows
International Journal for Numerical Methods in Fluids ( IF 1.7 ) Pub Date : 2020-12-07 , DOI: 10.1002/fld.4949
Nilesh Potghan ₁ , C. S. Jog ₁

Affiliation

In this work, we develop a numerical strategy for solving two‐phase immiscible incompressible fluid flows in a general arbitrary Lagrangian–Eulerian framework. As we use a conforming mesh moving with one of the fluids, there is no need to track or reconstruct the interface explicitly. A sharp interface, discontinuity in the fluid properties, and the jump in the pressure field are all accurately modeled using the dummy‐node technique. One of the challenges that this work addresses is to obtain a C⁰‐continuous approximation for the surface tension force term on the reference configuration, and to obtain its consistent linearization within the context of a Newton–Raphson strategy. It is shown by means of various numerical examples that the strategy is computationally efficient and robust, and circumvents the need for remeshing upto significantly large deformations.

中文翻译：

基于任意拉格朗日-欧拉方程的有限元策略，用于建模不可压缩的两相流

在这项工作中，我们开发了一种数值策略，用于在一般的任意拉格朗日-欧拉框架下求解两相不可混溶的不可压缩流体流。由于我们使用随流体之一移动的顺应网格，因此无需显式跟踪或重构界面。尖锐的界面，流体特性的不连续性以及压力场的跳跃都可以通过虚拟节点技术精确建模。这项工作要解决的挑战之一是获得C ⁰在参考配置上对表面张力项进行连续逼近，并在牛顿-拉夫森策略的背景下获得一致的线性化。通过各种数值示例表明，该策略在计算上是有效且稳健的，并且避免了对重新划分为明显较大变形的需求。

更新日期：2020-12-07

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