A volume-conservative PLIC algorithm on three-dimensional fully unstructured meshes

The PLIC (Piecewise Linear Interface Calculation) algorithm is one of the volume-of-fluid algorithms, which is highly efficient for the numerical simulations of gas-liquid interfacial flows. However, the PLIC algorithm needs complicated geometrical calculations for the reconstructions of the interfaces in interfacial cells, and therefore, the PLIC algorithm on unstructured meshes have not been studied enough. In this paper, the authors propose a new PLIC algorithm on unstructured meshes with arbitrary-shaped cells. In the proposed PLIC algorithm, several methods are developed or implemented to calculate the unit vector normal to an interface, the reconstruction of the interface and the surface tension. In addition, the volume fraction transport is improved by developing a volume-conservative algorithm in which gas and liquid volumes are conserved perfectly during the transport. As a result of the verification and validation tests, it is confirmed that the proposed PLIC algorithm enables the numerical simulations of interfacial dynamic behaviors with high accuracy even on unstructured meshes with highly-irregular cell arrangement. Finally, the proposed PLIC algorithm is applied to a dam-break problem and succeeds in reproducing the interfacial motion.