VolumeofFluid

Volume of Fluid (VOF) is a numerical method in computational fluid dynamics used to track the interface between immiscible fluids in two‑phase flows. The distribution is represented by a scalar field called the volume fraction, α, defined in each computational cell. α ranges from 0 to 1, with α=1 meaning the cell is full of fluid A, α=0 meaning fluid B, and 0<α<1 indicating an interface within the cell.

The Navier–Stokes equations are solved for a mixture, using α-weighted properties. Densities and viscosities are computed from α. The volume fraction is advected by the velocity field via ∂α/∂t + ∇·(u α) = 0 for incompressible flow. This approach allows tracking a moving free surface without explicit surface geometry.

A key feature is interface reconstruction in mixed cells. The most common approach is Piecewise Linear Interface Calculation (PLIC), which fits a plane to approximate the interface inside each cell, enabling accurate flux computation during advection. Other schemes include geometric reconstruction and flux limiting techniques to preserve mass.

VOF is widely used for air–water flows, bubble and droplet dynamics, ship wave simulations, inkjet printing, and other free-surface problems. It can be coupled with surface-tension models and, in some implementations, combined with level set methods (CLSVOF) to improve interface sharpness.

Limitations include numerical diffusion that thickens the interface, sensitivity to grid resolution, and challenges in representing highly curved or topologically complex interfaces. Advancements include sharpening schemes and variants such as THINC/VOF, SLIC/VOF, and CLSVOF. Volume of Fluid was introduced by Hirt and Nichols in 1981.