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arXiv:2301.04923 [math.NA]AbstractReferencesReviewsResources

Semi-Lagrangian Finite-Element Exterior Calculus for Incompressible Flows

Wouter Tonnon, Ralf Hiptmair

Published 2023-01-12Version 1

We develop a mesh-based semi-Lagrangian discretization of the time-dependent incompressible Navier-Stokes equations with free boundary conditions recast as a non-linear transport problem for a momentum 1-form. A linearly implicit fully discrete version of the scheme enjoys excellent stability properties in the vanishing viscosity limit and is applicable to inviscid incompressible Euler flows. Conservation of energy and helicity are enforced separately.

Comments: 35 pages, 23 figures
Categories: math.NA, cs.NA
Subjects: 65M60, 65D99, G.1.8
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