VOFs

Volume of Fluid methods (VOFs) are a class of numerical techniques used to track the interface between immiscible fluids in computational fluid dynamics. They were introduced by Hirt and Nichols in 1981 and represent fluid phases with a scalar volume fraction field α defined in each computational cell: α=1 for fluid A, α=0 for fluid B, and 0<α<1 in cells containing the interface.

The volume fraction is advected with the flow and coupled to the momentum equations. The fundamental equation is ∂α/∂t + ∇·(u α) = 0, ensuring conservation of mass for each phase. The interface is reconstructed within mixed cells, typically using Piecewise Linear Interface Calculation (PLIC). The reconstructed surface guides flux computations across cell faces to maintain a sharp, conserved interface during advection. Variants and hybrids are common, including methods that blend VOF with level-set information.

There are several notable extensions and schemes. CLSVOF combines Volume of Fluid with a level-set function to improve curvature estimation and surface tension treatment. THINC (Tangent of Hyperbolic Circle) and isoAdvector offer alternative interface-capturing and advection approaches. Modern implementations frequently blend methods to enhance accuracy, robustness, and efficiency, especially on unstructured meshes.

VOFs are well suited to problems with large density and viscosity contrasts and complex interface topologies, but they face challenges such as numerical diffusion of the interface, mass conservation in long-time simulations, and the handling of surface tension–driven flows, which can induce spurious currents if not discretized carefully. Applications span two-phase flows, droplets and bubbles, jets, boiling, and cavitation. Widely used software includes OpenFOAM, Basilisk, Gerris, and various commercial CFD codes.