The physical requirement that there can be no mass flux through the free
surface, gives a kinematic boundary condition that has to be fulfilled at
the surface. The condition states that the boundary has to move as a material
surface, and is written as

(5)

where is the location of the free surface.

A dynamic condition has also to be fulfilled at the surface. This condition
states that the momentum across the free surface has to be conserved,

(6)

where is the stress tensor

(7)

is the surface tension, the surface curvature, p_{atm} the atmospheric
pressure, n_{i} is the unit normal vector
directed outwards of the surface. If the surface tension is neglected and the
flow is considered non viscous, the dynamic condition can be simplified to

(8)

The corresponding boundary condition for , Eq.(3) becomes