  A conservative primitive variable discrete exterior calculus (DEC)
discretization of the Navier-Stokes equations is performed. An existing DEC
method (Mohamed, M. S., Hirani, A. N., Samtaney, R. (2016). Discrete exterior
calculus discretization of incompressible Navier-Stokes equations over surface
simplicial meshes. Journal of Computational Physics, 312, 175-191) is modified
to this end, and is extended to include the energy-preserving time integration
and the Coriolis force to enhance its applicability to investigate the late
time behavior of flows on rotating surfaces, i.e., that of the planetary flows.
The simulation experiments show second order accuracy of the scheme for the
structured-triangular meshes, and first order accuracy for the otherwise
unstructured meshes. The method exhibits second order kinetic energy relative
error convergence rate with mesh size for inviscid flows. The test case of flow
on a rotating sphere demonstrates that the method preserves the stationary
state, and conserves the inviscid invariants over an extended period of time.
