Spline Representation of Incompressible Flow

We describe a scheme for reconstructing a distribution of fluidvelocities from given values of the net flow across the facesof a rectangular mesh in two or three dimensions. Assuming thedata to be consistent, the reconstructed velocities will havethe properties that the continuity condition is everywhere satisfied,that the track of any fluid particle is a smooth curve and thatthere is no flow across any part of the boundary that has beenspecified as representing a solid wall.