A Multi-Scale Volume of Fluid Method Enabled by Hybrid Interface Reconstructions

The geometric Volume of Fluid (VOF) method uses a sharp fluid-fluid interface reconstruction to improve phase advection and curvature calculation. Traditional single plane reconstructions (PLIC) perform well for low-curvature interfaces, while newer two-plane reconstructions (R2P) and paraboloid reconstructions (PPIC) enable thin film or higher curvature reconstructions. To efficiently and accurately simulate multi-scale flows such as liquid atomization, a robust VOF method should automatically select a grid cell's best reconstruction from the available interface geometries.

In this work, we demonstrate a hybrid reconstruction method composed of PLIC, PPIC, R2P, and a novel cylinder reconstruction. PLIC and PPIC are used for resolved cases, R2P handles sub-grid thin films, and cylinders represent sub-grid fluid ligaments. The cylinder reconstruction method fits a quadratic principal curve to local phasic barycenter data to locate and orient a cylinder, and the radius is then chosen to conserve volume. On-the-fly ligament detection is done using connected-component labeling with the moments of inertia of the volume fractions, while thin films are detected with the sub-grid misalignment of transported surface normals. This feature detection is then used for the automated selection of a cell's interface reconstruction, which enables a multi-scale VOF scheme that is tested in several multiphase simulations.