  A novel numerical technique designed for interface flow simulations using the
Volume of Fluid (VOF) method on arbitrary unstructured meshes has been
introduced. The method is called SimPLIC, which seamlessly integrates Piecewise
Linear Interface Calculation (PLIC) and Simpson's rule. The main focus of the
proposed method is to compute the volume of the primary phase that moves across
a mesh face within a single time step. This is achieved by reconstructing the
interface and assessing how the submerged face area evolves over time.
Simpson's rule is employed to integrate the time evolution of this submerged
face area, ensuring an accurate estimation of the volume of the transported
primary phase. The method's robustness was validated by solving a spherical
interface advection problem in a non-uniform three-dimensional flow across
unstructured meshes with diverse cell types and dimensions. Key metrics such as
volume conservation, shape retention, friction boundedness and solving
efficiency were meticulously monitored and juxtaposed. Numerical outcomes
underscored the precision and adequacy of the PLIC-VOF technique when
complemented with Simpson's rule in advecting the interface. Furthermore, the
SimPLIC method has been integrated into OpenFOAM v2312 as an unofficial
extension and is now accessible to the community.
