A coupled level set and volume of fluid method with a re-initialisation step suitable for unstructured meshes

This paper presents a coupling method of the level set and volume of fluid methods based on a simple local-gradient based re-initialisation approach that evaluates the distance function depending on the computational cell location. If a cell belongs to the interface, the signed distance is updated based on a search in the neighbouring cells and an interpolation procedure is applied depending on the local curvature or the sign of the level set function following [41]. The search algorithm does not distinguish between the upwind and downwind directions and hence it is able to be used for cells with an arbitrary number of faces increasing the robustness of the method. The coupling with the volume of fluid method is achieved by mapping the volume fraction field which is advected from the isoface evolution at a subgrid level. Consequently, the coupling with the level set approach is utilised without solving the level set equation. This coupled method provides better accuracy than the volume of fluid method alone and is capable of capturing sharp interfaces in all the classical numerical tests that are presented here