摘要：The level-set method has become a popular approach to tackle two-phase, incompressible flow problems. In the standard level-set method the equations are solved in both fluids with smoothed fluid properties across the interface. In contrast to the standard level set method, the single-phase level set method is concerned with the solution of the flow field in the denser phase only. Some of the advantages of such an approach are that the interface remains sharp, the computation is performed within a fluid with uniform properties and that only minor computations are needed in the air. The location of the interface is determined using a signed distance function, exactly as done on the standard level-set method, but appropriate interpolations and extrapolations are used at the fluid/fluid interface to enforce the jump conditions. In our RANS solver with non-orthogonal grids, very large cell aspect ratios appear on the near-wall regions of the flow, which causes the standard reinitialization methods to fail. To overcome this problem, a reinitialization procedure has been developed that works well with non-orthogonal grids with large aspect ratios. Since the grid points in air don’t have a well defined velocity, the time derivatives cannot be treated in the Eulerian fashion in points that change from air to water during a time step. This problem is dealt with by using a convective extension to obtain the velocities at previous time-steps for the grid points in air, which provides a good estimation of the total derivatives. In this paper we discuss the details of such implementations. The method was applied to two unsteady tests: sloshing in a two-dimensional tank and wave diffraction in a surface ship, and the results compared against analytical solutions or experimental data. The method can in principle be applied to any problem in which the standard level-set method works, as long as the stress on the second phase can be specified and no bubbles appear in the flow during the computation.
其他摘要：The level-set method has become a popular approach to tackle two-phase, incompressible flow problems. In the standard level-set method the equations are solved in both fluids with smoothed fluid properties across the interface. In contrast to the standard level set method, the single-phase level set method is concerned with the solution of the flow field in the denser phase only. Some of the advantages of such an approach are that the interface remains sharp, the computation is performed within a fluid with uniform properties and that only minor computations are needed in the air. The location of the interface is determined using a signed distance function, exactly as done on the standard level-set method, but appropriate interpolations and extrapolations are used at the fluid/fluid interface to enforce the jump conditions. In our RANS solver with non-orthogonal grids, very large cell aspect ratios appear on the near-wall regions of the flow, which causes the standard reinitialization methods to fail. To overcome this problem, a reinitialization procedure has been developed that works well with non-orthogonal grids with large aspect ratios. Since the grid points in air don’t have a well defined velocity, the time derivatives cannot be treated in the Eulerian fashion in points that change from air to water during a time step. This problem is dealt with by using a convective extension to obtain the velocities at previous time-steps for the grid points in air, which provides a good estimation of the total derivatives. In this paper we discuss the details of such implementations. The method was applied to two unsteady tests: sloshing in a two-dimensional tank and wave diffraction in a surface ship, and the results compared against analytical solutions or experimental data. The method can in principle be applied to any problem in which the standard level-set method works, as long as the stress on the second phase can be specified and no bubbles appear in the flow during the computation.
