Lattice hydrodynamics

We make use of the combinatorics of two interlocking face centered cubic lattices to make a discrete vector calculus which allows construction of two models of incompressible fluid motion in periodic three space, one based on momentum conservation and one based on the principle of vorticity transport. Without taking the calculus limit, one nevertheless arrives in the vector calculus language to the exact writings of the continuum model, the first due to Jean Leray with the derivative on the outside of the nonlinear term and then the familiar form with the derivative on the inside. Numerical studies show these two models are different at the discrete level.