A high-resolution characteristics-based implicit dual time-stepping VOF method for free surface flow simulation on unstructured grids

In this paper, a new unstructured-grid/finite volume incompressible Navier-Stokes solver, based on a high-order characteristics-based method, the artificial compressibility method, and a matrix-free implicit dual time-stepping scheme, has been developed to study unsteady free surface flows. The free surface effects are calculated using the volume of fluid (VOF) method and continuum surface force. The transport equation for the VOF is numerically solved using exactly the same method for the flow solver. A number of test cases have been studied to validate the proposed method and demonstrate its capability by comparison with other schemes and published results.