We begin with the incompressible form of the momentum equation. The equation has been divided through by the density (P = p/ρ) and density has been absorbed into the body force term.
The equation is integrated over the control volume of a computational cell.
The time-dependent term and the body force term are assumed constant over the volume of the cell. The divergence theorem is applied to the advection, pressure gradient, and diffusion terms.
where n is the normal of the surface of the control volume and V is the volume. If the control volume is a polyhedron and values are assumed constant over each face, the area integrals can be written as summations over each face.
where the subscript nbr denotes the value at any given face.