In this work, an extended discontinuous Galerkin (extended DG/XDG also called unfitted DG) solver for two-dimensional flow problems exhibiting moving contact lines is presented. The generalized Navier boundary condition is employed within the XDG discretization for the handling of the moving contact lines. The spatial discretization is based on a symmetric interior penalty method and the numerical treatment of the surface tension force is done via the Laplace–Beltrami formulation. The XDG method adapts the approximation space conformal to the position of the interface and allows a sub-cell accurate representation within the 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. No adaption of the level-set evolution algorithm is needed for the extension to moving contact line problems. The developed solver is validated against typical two-dimensional contact line driven flow phenomena including droplet simulations on a wall and the two-phase Couette flow.

中文翻译：

---

基于广义Navier边界条件适用于移动接触线问题的扩展不连续Galerkin方法

在这项工作中，提出了一种用于显示移动接触线的二维流动问题的扩展不连续 Galerkin（扩展 DG/XDG 也称为未拟合 DG）求解器。XDG 离散化中采用广义 Navier 边界条件来处理移动接触线。空间离散化基于对称内部惩罚方法，表面张力的数值处理通过 Laplace-Beltrami 公式完成。XDG 方法使近似空间与界面位置共形，并允许在锐界面公式中准确表示子单元。该接口被描述为有符号距离水平集函数的零集，并通过标准 DG 方法进行离散化。对于移动接触线问题的扩展，不需要调整水平集演化算法。开发的求解器针对典型的二维接触线驱动的流动现象进行了验证，包括壁上的液滴模拟和两相 Couette 流。