论文标题
使用拟合和未固定方法的两相纳维尔 - 斯托克斯对结构的离散化
Structure-preserving discretizations of two-phase Navier-Stokes flow using fitted and unfitted approaches
论文作者
论文摘要
我们考虑了两相流的尖锐接口模型的数值近似，该模型由散装域中不可压缩的Navier-Stokes方程以及接口上的经典接口条件给出。我们为模型提出了具有结构的有限元方法，这特别是在离散级别上满足体积保存和能量衰减。对于不断发展的流体界面，我们采用参数有限元近似值，引入了隐式切向速度以提高接口网格的质量。对于两阶段Navier-Stokes方程，我们考虑了两种不同的方法：分别是一种未拟合和拟合的有限元方法。在未实现的方法中，构造的方法基于欧拉弱的表述，而在拟合的方法中，引入了新型的任意拉格朗日 - 欧拉（ALE）弱公式。使用这两种公式的合适离散化，我们介绍了两种有限元方法，并证明了它们的结构保存属性。提出了数值结果，以显示引入方法的准确性和效率。
We consider the numerical approximation of a sharp-interface model for two-phase flow, which is given by the incompressible Navier-Stokes equations in the bulk domain together with the classical interface conditions on the interface. We propose structure-preserving finite element methods for the model, meaning in particular that volume preservation and energy decay are satisfied on the discrete level. For the evolving fluid interface, we employ parametric finite element approximations that introduce an implicit tangential velocity to improve the quality of the interface mesh. For the two-phase Navier-Stokes equations, we consider two different approaches: an unfitted and a fitted finite element method, respectively. In the unfitted approach, the constructed method is based on an Eulerian weak formulation, while in the fitted approach a novel arbitrary Lagrangian-Eulerian (ALE) weak formulation is introduced. Using suitable discretizations of these two formulations, we introduce two finite element methods and prove their structure-preserving properties. Numerical results are presented to show the accuracy and efficiency of the introduced methods.
