An adaptive coupled volume-of-fluid and level set method based on unstructured grids

This paper presents an adaptive coupled volume-of-fluid and level set (VOSET) method based on unstructured grids to simulate incompressible interfacial flows. In this study, a novel high quality refinement algorithm for unstructured grid cells based on level set and surface curvature is first developed to ensure a preset bandwidth of the adaptive region around the interface. Subsequently, the adaptive VOSET algorithm is integrated into a finite volume solver with a large-scale sparse matrix preconditioned bi-stable conjugate method. Finally, the accuracy and robustness of the current method are validated by four classical test cases: the dam break, single bubble rising, a Rayleigh–Taylor instability problem, and a liquid jet problem. It is found that the adaptive coupled VOSET algorithm makes the numerical results near the interface more accurate, especially the curvature and surface tension at corners. Moreover, the adaptive VOSET is more efficient since it reduces the number of grid cells significantly. The present results show that only 4.85%–24.5% of the number of adaptive grid cells and 5.31%–15.93% of the computational time are needed for VOSET compared to that of fixed unstructured grid cells, and thus, it has outstanding properties of both time and computational cost savings.