A One-Cell Local Multigrid Method for Solving Unsteady Incompressible Multiphase Flows

An original local multigrid method for solving incompressible two-phase flow with surface tension is described. The dynamics of the interface are resolved on a hierarchy of structured and uniform grids (orthogonal Cartesian meshes). A new type of composite boundary condition is proposed to solve the dynamics of the multigrid calculation domains. The interface tracking is described by a TVD VOF algorithm and the equations of motion are solved using an augmented Lagrangian method. The surface tension is calculated using a continuous surface force method. The one-cell local multigrid method is compared to relevant analytical scalar advection tests. Several classical two-phase flow problems, including nonlinear drop oscillations, Rayleigh–Taylor instabilities, and the drop impact on liquid film, have also been considered. The local character of the method and the differences between a single-grid and a multigrid solution are discussed. For unsteady problems, such as the Rayleigh–Taylor instability, the memory costs and the computational time have been reduced by up to 50%.