论文标题
关于不可压缩的两相流的扩展不连续的盖尔金方法的行进级别方法
On a marching level-set method for extended discontinuous Galerkin methods for incompressible two-phase flows
论文作者
论文摘要
在这项工作中，提出了基于扩展的不连续Galerkin（扩展DG/XDG）方法的求解器。 XDG方法适应近似空间与接口的位置相吻合。这允许在其尖锐的界面配方中对不可压缩的Navier-Stokes方程进行子单元的准确表示。该界面被描述为符号距离级别函数的零集，并通过标准DG方法离散。对于界面，resp。级别，进化的级别，使用了扩展速度场，并为其在狭窄带上的构造中提出了两阶段算法。在切割细胞上，单层椭圆延伸速度方法进行了调整，并在相邻的细胞上进行了快速密切的过程。空间离散化基于一种对称内部惩罚方法，对于时间离散化，移动接口方法是适应的。细胞聚集技术用于处理界面运动过程中的小型切口和拓扑变化。该方法通过广泛的典型的两相张力表面驱动流动现象（包括毛细管波，振荡液滴和上升的气泡基准）进行验证。
In this work a solver for instationary two-phase flows on the basis of the extended Discontinuous Galerkin (extended DG/XDG) method is presented. The XDG method adapts the approximation space conformal to the position of the interface. This allows a sub-cell accurate representation of the incompressible Navier-Stokes equations in their sharp interface formulation. The interface is described as the zero set of a signed-distance level-set function and discretized by a standard DG method. For the interface, resp. level-set, evolution an extension velocity field is used and a two-staged algorithm is presented for its construction on a narrow-band. On the cut-cells a monolithic elliptic extension velocity method is adapted and a fast-marching procedure on the neighboring cells. The spatial discretization is based on a symmetric interior penalty method and for the temporal discretization a moving interface approach is adapted. A cell agglomeration technique is utilized for handling small cut-cells and topology changes during the interface motion. The method is validated against a wide range of typical two-phase surface tension driven flow phenomena including capillary waves, an oscillating droplet and the rising bubble benchmark.
