  A conservative discretization of incompressible Navier-Stokes equations is
developed based on discrete exterior calculus (DEC). A distinguishing feature
of our method is the use of an algebraic discretization of the interior product
operator and a combinatorial discretization of the wedge product. The governing
equations are first rewritten using the exterior calculus notation, replacing
vector calculus differential operators by the exterior derivative, Hodge star
and wedge product operators. The discretization is then carried out by
substituting with the corresponding discrete operators based on the DEC
framework. Numerical experiments for flows over surfaces reveal a second order
accuracy for the developed scheme when using structured-triangular meshes, and
first order accuracy for otherwise unstructured meshes. By construction, the
method is conservative in that both mass and vorticity are conserved up to
machine precision. The relative error in kinetic energy for inviscid flow test
cases converges in a second order fashion with both the mesh size and the time
step.
