Semi-Lagrangian Finite-Element Exterior Calculus for Incompressible Flows
Numerical Analysis
2024-02-05 v2 Numerical Analysis
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.
Keywords
Cite
@article{arxiv.2301.04923,
title = {Semi-Lagrangian Finite-Element Exterior Calculus for Incompressible Flows},
author = {Wouter Tonnon and Ralf Hiptmair},
journal= {arXiv preprint arXiv:2301.04923},
year = {2024}
}
Comments
Submitted to Advances in Computational Mathematics (ACM), Topical Collection on Systematic Exploitation of Structural Properties in Electromagnetism