Full-variable Cartesian grid method for incompressible and multiphase flows

Abstract

We propose an efficient incompressible fluid solver based on a Cartesian grid and multi-moment concept. In the proposed method, velocity variables are located at cell centers, face centers and nodes in 2D, and cell centers, face centers, edge centers and nodes in 3D but the pressure variables are located only at the cell centers. The Cartesian grid is called full-variable Cartesian grid (FVCG) and the proposed method is called FVCG method. By using the FVCG method, we could improve velocity calculations (error reduction and numerical oscillation suppression) without significant increase in computational time. For instance, in a 3D multiphase flow simulation, although the FVCG method uses twice velocity resolution compared to existing methods, the increase in computational time was only 2%-9%. The FVCG method was validated through various benchmark problems, and comparisons with experiments of coalescence and separations of two liquid droplets (three different cases) and droplet splashing on a superhydrophobic substrate. These numerical results have shown that the FVCG method can efficiently simulate incompressible flows and free surface flows which involve highly complex surface topology changes with coarse grids. These numerical results have also shown that the FVCG method is robust.