A piecewise linear interface-capturing volume-of-fluid method based on unstructured grids

A piecewise linear interface calculation (PLIC) technique on triangular unstructured grids is proposed for the volume-of-fluid (VOF) method. For an interface cell, a straight line segment is set to approximate the actual interface by the gradient of the volume fraction function. Three gradient models are discussed, and the results show that the gradient model introduced from the moving particle semi-implicit method is of the highest accuracy. Mass flux is calculated in a Eulerian scheme depending on the relationship between the line segment and each boundary of the cell. It is proved that the combination of geometric and algebraic methods is most precise, because both geometric interface position and algebraic mass conservation are considered. Numerical experiments are conducted on unstructured grids generated by the traditional Delaunay triangulation method and the bubble packing method (BPM), which can produce much more regular triangular cells than the Delaunay method (see Wu and Chen, Numerical Heat Transfer B, vol. 58; pp. 343-369, 2010). Compared with Young's PLIC-VOF, our method is of satisfactory accuracy and sharpness. The deformation errors on the BPM grid are even smaller than those by the PLIC method on a structured grid. In addition, it is observed that the accuracy is higher on the unstructured grid, with better quality.