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An analytical interface reconstruction algorithm in the PLIC‐VOF method for 2D polygonal unstructured meshes

Piecewise linear interface calculation (PLIC) schemes have been extensively employed in the volume‐of‐fluid (VOF) method for interface capturing in numerical simulations of multiphase flows. Polygonal unstructured meshes are often adopted because of their geometric flexibility and superiority in gradient calculation. An analytical interface reconstruction algorithm in the PLIC‐VOF method for arbitrary convex polygonal cells has been proposed in this study. The line interface at a given orientation within a polygonal cell is located by an analytical technique. It has been tested successfully for four different geometric shapes that are common in polygonal meshes. The computational efficiency of the present algorithm has been compared with several published schemes in the literature. The proposed algorithm has been shown to yield higher accuracy with reduction in computational complexity. A numerical simulation of a dam‐breaking problem has been performed using the proposed analytical PLIC technique on polygonal meshes. The results are in good agreement with experimental data available in the literature, which serves as a demonstration of its performance in a real multiphase flow.