论文标题
具有非结构化各向异性网状适应性的高阶有限元方法，用于表面张力
A higher-order finite element method with unstructured anisotropic mesh adaption for two phase flows with surface tension
论文作者
论文摘要
提出了一个新颖的有限元框架，用于对表面张力的两个相流进行数值模拟。为了在具有光滑界面的区域中，使用液态加速器界面的液位二次插值（P2）插值的水平集（LS）方法。连续性表面力模型的平衡力实现用于考虑表面张力并尽可能准确地解决静态问题。鉴于这需要在用于LS函数的离散化和用于压力场的离散化之间的平衡，因此为Navier-Stokes和LS Advection方程提出了相等的P2/P2/P2方案，这些方程与彼此强烈耦合。使用基于残差的变分多尺度框架稳定这种完全隐式的公式。为了提高准确性并获得最少数量的元素的最佳收敛速率，建议提出各向异性网状适应方法，其中将非结构化的网格保持在尽可能靠近P2 LS函数的零ISO-VALUE时保持罚款。元素在具有平坦接口的区域自动拉伸，以使模拟过程中的复杂性保持固定。对于上升气泡的两维模拟，证明了这种方法的准确性和效率。
A novel finite element framework is proposed for the numerical simulation of two phase flows with surface tension. The Level-Set (LS) method with piece-wise quadratic (P2) interpolation for the liquid-gas interface is used in order to reach higher-order convergence rates in regions with smooth interface. A balanced-force implementation of the continuum surface force model is used to take into account the surface tension and to solve static problems as accurately as possible. Given that this requires a balance between the discretization used for the LS function, and that used for the pressure field, an equal-order P2/P2/P2 scheme is proposed for the Navier-Stokes and LS advection equations, which are strongly coupled with each other. This fully implicit formulation is stabilized using the residual-based variational multiscale framework. In order to improve the accuracy and obtain optimal convergence rates with a minimum number of elements, an anisotropic mesh adaption method is proposed where the unstructured mesh is kept as fine as possible close to the zero iso-value of the P2 LS function. Elements are automatically stretched in regions with flat interface in order to keep the complexity fixed during the simulation. The accuracy and efficiency of this approach are demonstrated for two and three dimensional simulations of a rising bubble.
