A horizontal refined piecewise linear interface reconstruction (HOPLIRE) method based on the VOSET method for capturing the two-phase interface

Abstract

The interface reconstruction method is significant for the numerical research of the two-phase problem, but the implementation of popular ones is not easy enough. In this paper, a horizontal refined piecewise linear interface reconstruction (HOPLIRE) method with a straightforward implementation procedure is proposed for the incompressible flow, and the idea of that is to reconstruct the two-phase interface in one grid cell with many horizontal refined pieces. Only one situation without complex classifications needs to be considered for reconstructing the interface, and the volume fraction flux through the grid cell face can be easily obtained to solve the VOF function by a simple four fundamental operations of arithmetic. In addition to the advantages of simple implementation for the HOPLIRE method, the accuracy of the reconstructed vapor–liquid interface is also high. The proximity between the HOPLIRE method and the popular piecewise linear interface reconstruction (PLIC) method increases with the divided piece number of the HOPLIRE method, and 30 is recommended based on calculation accuracies of LS function, interface direction, and curvature. Besides, the good performances of the VOSET-HOPLIRE method in the calculation accuracy and efficiency are verified by comparing with VOF-PLIC and VOSET-PLIC methods by some classical two-phase problems. Currently, the HOPLIRE method is only presented based on a two-dimensional problem under a structured mesh. In the future, this methodology will be improved to cover three-dimensional problems and unstructured meshes.