In this study, a numerical model for simulating two-phase flow is developed. The Cartesian grid with Adaptive Mesh Refinement (AMR) is adopted to reduce the computational cost. An explicit projection method is used for the time integration and the Finite Difference Method (FDM) is applied on a staggered grid for the discretization of spatial derivatives. The Volume of Fluid (VOF) method with Piecewise-Linear Interface Calculation (PLIC) is extended to the AMR grid to capture the gas-water interface accurately. A coarse-fine interface treatment method is developed to preserve the flux conservation at the interfaces. Several two-dimensional (2D) and three-dimensional (3D) benchmark cases are carried out for the validation of the model. 2D and 3D shear flow tests are conducted to validate the extension of the VOF method to the AMR grid. A 2D linear sloshing case is considered in which the model is proved to have 2nd-order accuracy in space. The efficiency of applying the AMR grid is discussed with a nonlinear sloshing problem. Finally, 2D solitary wave past stage and 2D/3D dam break are simulated to demonstrate that the model is able to simulate violent interface problems.

Two-phase flow; adaptive mesh refinement; VOF; coarse-fine interface treatment