Real flows often consist of 'active' regions of concentrated vorticity (close to boundary layers or liquid-liquid interfaces) or sharp change of physical quantities (close to flame fronts), and more 'passive' regions where the flow is more uniform. The adaptive grid method utilises fine grids in the 'active' regions and coarse grids in the 'passive' regions. It dramatically improves the computational performance.
Fig. 1. Rising oil droplet (red solid line) breaking through air-water interface (green dashed-line) (left) and a close-up (right).