Data from: A computational method for sharp interface advection

We devise a numerical method for passive advection of a surface, such as the interface between two incompressible fluids, across a computational mesh. The method is called isoAdvector, and is developed for general meshes consisting of arbitrary polyhedral cells. The algorithm is based on the volume of fluid (VOF) idea of calculating the volume of one of the fluids transported across the mesh faces during a time step. The novelty of the isoAdvector concept consists in two parts: First, we exploit an isosurface concept for modelling the interface inside cells in a geometric surface reconstruction step. Second, from the reconstructed surface, we model the motion of the face-interface intersection line for a general polygonal face to obtain the time evolution <i>within</i> a time step of the submerged face area. Integrating this submerged area over the time step leads to an accurate estimate for the total volume of fluid transported across the face. The method was tested on simple 2D and 3D interface advection problems both on structured and unstructured meshes. The results are very satisfactory both in terms of volume conservation, boundedness, surface sharpness, and efficiency. The isoAdvector method was implemented as an OpenFOAM® extension and is published as open source.

我们提出了一种可实现计算网格上曲面被动输运的数值方法，此类曲面可指代两种不可压缩流体间的分界面。该方法命名为isoAdvector，专为包含任意多面体单元的通用网格体系设计。本算法基于流体体积法（Volume of Fluid, VOF）的核心思想，即计算单个流体在单时间步内穿过网格面的输运体积。isoAdvector方法的创新之处分为两点：其一，在几何曲面重构步骤中，采用等值面（isosurface）概念对单元内部的分界面进行建模；其二，基于重构得到的曲面，针对通用多边形网格面，对网格面与分界面的交线运动进行建模，以此得到单时间步内淹没面面积的时间演化过程。将该淹没面面积在时间步长内积分，即可精准估算穿过该网格面的流体总输运体积。我们分别在结构化与非结构化网格上的二维、三维简单分界面输运问题中对该方法进行了测试，测试结果在体积守恒性、有界性、曲面清晰度与计算效率等方面均表现优异。isoAdvector方法已作为OpenFOAM®的扩展插件实现，并以开源形式发布。