A primitive variable discrete exterior calculus discretization of incompressible Navier–Stokes equations over surface simplicial meshes

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