Discrete Exterior Calculus Discretization of the Incompressible Navier-Stokes Equations

Speaker: Ravi Samtaney, the King Abdullah University of Science and Technology (KAUST)
July 30, 2015

Presentation

Abstract

A conservative discretization of Navier-Stokes equations on simplicial meshes is developed based on discrete exterior calculus (DEC). 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 the corresponding discrete operators based on the DEC framework. Numerical tests will be presented for flows on flat and curved 2D domains. Our simulations 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 the mass and the 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.

Biography

Ravi Samtaney is presently a professor in Mechanical Engineering (Physical Science and Engineering Division) with a joint appointment in Applied Mathematics & Computational Science at the King Abdullah University of Science and Technology (KAUST) in Saudi Arabia. He serves as Chair of the ME Program and Associate Dean of the PSE Division. Prior to KAUST, he was a Research Physicist at the Princeton Plasma Physics Laboratory, Princeton University, and a research faculty at the California Institute of Technology, and worked at NASA Ames Research Center. His research is at the intersection of applied mathematics, physics, and engineering, from fundamental processes in fluid mechanics (shocks, turbulence, ablation, ionization, etc.) to numerical methods and large-scale computing (adaptive meshing, scalable solvers, software engineering, etc.). He obtained his Ph.D. from Rutgers University in 1994.

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