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

✍ Scribed by Stéphane Vincent; Jean-Paul Caltagirone

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 545 KB
• Volume: 163
• Category: Article
• ISSN: 0021-9991
• DOI: 10.1006/jcph.2000.6566

✦ Synopsis

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 onecell 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 singlegrid 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%.