A one-cell local multigrid method for solving unsteady incompressible multiphase flows

An original local multigrid method for solving incompressible two-phase flo w with surface tension is described. The dynamics of the interface are reso lved on a hierarchy of structured and uniform grids (orthogonal Cartesian m eshes). A new type of composite boundary condition is proposed to solve the dynamics of the multigrid calculation domains. The interface tracking is d escribed by a TVD VOF algorithm and the equations of motion are solved usin g an augmented Lagrangian method. The surface tension is calculated using a continuous surface force method. The one-cell local multigrid method is co mpared to relevant analytical scalar advection tests. Several classical two -phase How problems, including nonlinear drop oscillations, Rayleigh-Taylor instabilities, and the drop impact on liquid film, have also been consider ed. 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 ti me have been reduced by up to 50%. (C) 2000 Academic Press.