A Primitive Variable Discrete Exterior Calculus Discretization of Incompressible Navier-Stokes Equations over Surface Simplicial Meshes

Abstract

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.

References in corpus (6)

• Vortices in Superfluid Films on Curved Surfaces
• Discrete Exterior Calculus
• Discrete exterior calculus discretization of incompressible Navier-Stokes equations over surface simplicial meshes
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• Discrete exterior calculus (DEC) for the surface Navier-Stokes equation
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Cited by in corpus (3)

• Geometric and energy-aware decomposition of the Navier-Stokes equations: A port-Hamiltonian approach
• Discrete exterior calculus discretization of two-phase incompressible Navier-Stokes equations with a conservative phase field method
• Effects of Rotation on Vorticity Dynamics on a Sphere with Discrete Exterior Calculus