An unfitted interior penalty discontinuous Galerkin method for incompressible Navier–Stokes two‐phase flow
An unfitted interior penalty discontinuous Galerkin method for incompressible Navier–Stokes two‐phase flow
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DOI：
10.1002/fld.3653
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发表时间：
2013-01
影响因子：
1.8
通讯作者：
Felix Heimann;C. Engwer;O. Ippisch;P. Bastian
中科院分区：
文献类型：
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作者：
Felix Heimann;C. Engwer;O. Ippisch;P. Bastian
提出了一种基于非对称内罚法求解非混相不可压缩两相流问题的不连续Galerkin方法。因此，求解了不可压缩区域的Navier-Stokes方程，该区域被分解为具有不同粘度和密度值的两个子区域，并且具有奇异表面张力。在界面分段线性逼近的基础上，从一个结构网格中切割出两个阶段的网格。不连续的有限元被定义在由此产生的笛卡尔切割单元网格上，因此可以高精度地近似压力和速度导数在界面上的不连续。当网格分解界面时，不需要对界面上的密度和粘度跳跃进行正则化。即使在界面附近，这也保留了速度场的局部守恒性质，与标准方法相比，这是一个显著的优势，标准方法需要对这些不连续进行正则化，并且不能表示压力和速度的跳跃和扭结。一个强大的细分算法被纳入允许使用标准时间积分器（如Crank-Nicholson）对时间相关的网格。所提出的离散化方法适用于二维和三维情况。我们的方法的性能通过应用于一个二维基准问题来证明，允许与其他数值方法进行彻底的比较。版权所有©2012 John Wiley & Sons， Ltd。
A discontinuous Galerkin method for the solution of the immiscible and incompressible two‐phase flow problem based on the nonsymmetric interior penalty method is presented. Therefore, the incompressible Navier–Stokes equation is solved for a domain decomposed into two subdomains with different values of viscosity and density as well as a singular surface tension force. On the basis of a piecewise linear approximation of the interface, meshes for both phases are cut out of a structured mesh. The discontinuous finite elements are defined on the resulting Cartesian cut‐cell mesh and may therefore approximate the discontinuities of the pressure and the velocity derivatives across the interface with high accuracy. As the mesh resolves the interface, regularization of the density and viscosity jumps across the interface is not required. This preserves the local conservation property of the velocity field even in the vicinity of the interface and constitutes a significant advantage compared with standard methods that require regularization of these discontinuities and cannot represent the jumps and kinks in pressure and velocity. A powerful subtessellation algorithm is incorporated to allow the usage of standard time integrators (such as Crank–Nicholson) on the time‐dependent mesh. The presented discretization is applicable to both the two‐dimensional and three‐dimensional cases. The performance of our approach is demonstrated by application to a two‐dimensional benchmark problem, allowing for a thorough comparison with other numerical methods. Copyright © 2012 John Wiley & Sons, Ltd.