In physics, a free surface flow is the surface of a fluid flowing that is subjected to both zero perpendicular normal stress and parallel shear stress. This can be the boundary between two homogeneous fluids, like water in an open container and the air in the Earth's atmosphere that form a boundary at the open face of the container.

Computation of free surfaces is complex because of the continuous change in the location of the boundary layer. Conventional methods of computation are insufficient for such analysis. Therefore, special methods are developed for the computation of free surface flows.

Computation in flows with free and moving boundaries like the open-channel flow is a difficult task. The position of the boundary is known only at the initial time and its location at later times can be determined as using various methods like the Interface Tracking Method and the Interface Capturing Method.

Neglecting the phase change at the free surface, the following boundary conditions apply.

The free surface should be a sharp boundary separating the two fluids. There should be no flow through this boundary, i.e.,

where the subscript ${\displaystyle \Box _{fs}}$ stands for free surface. This implies that the normal component of the velocity of the fluid at the surface is equal to the normal component of the velocity of the free surface.

The forces acting on the fluid at free surface should be in equilibrium, i.e. the momentum is conserved at the free surface. The normal forces on either side of the free surface are equal and opposite in direction and the forces in tangential direction should be equal in magnitude and direction.

Here σ is the surface tension, n, t and s are unit vectors in a local orthogonal coordinate system (n,t,s) at the free surface (n is outward normal to the free surface while the other two lie in the tangential plane and are mutually orthogonal). The indices 'l' and 'g' denote liquid and gas, respectively and K is the curvature of the free surface.