TL;DR
This paper introduces a semi-Lagrangian finite-element method for incompressible flows that ensures stability, energy, and helicity conservation, applicable to both viscous and inviscid regimes.
Contribution
It develops a novel mesh-based semi-Lagrangian discretization for Navier-Stokes equations using exterior calculus, with stability and conservation properties.
Findings
Stable in the vanishing viscosity limit
Applicable to inviscid Euler flows
Conserves energy and helicity
Abstract
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.
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