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

Pankaj Jagad, Abdullah Abukhwejah, Mamdouh Mohamed, Ravi Samtaney

Research output: Contribution to journalArticlepeer-review

Abstract

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 exterior calculus discretization of incompressible Navier–Stokes equations over surface simplicial meshes,” J. Comput. Phys. 312, 175–191 (2016)] 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 a 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.
Original languageEnglish (US)
Pages (from-to)017114
JournalPhysics of Fluids
Volume33
Issue number1
DOIs
StatePublished - Jan 1 2021

Fingerprint Dive into the research topics of 'A primitive variable discrete exterior calculus discretization of incompressible Navier–Stokes equations over surface simplicial meshes'. Together they form a unique fingerprint.

Cite this