A multimesh finite element method for the Navier-Stokes equations based on projection methods
Abstract
The multimesh finite element method is a technique for solving partial differential equations on multiple non-matching meshes by enforcing interface conditions using Nitsche's method. Since the non-matching meshes can result in arbitrarily cut cells, additional stabilization terms are needed to obtain a stable variational formulation. In this contribution we extend the multimesh finite element method to the Navier-Stokes equations based on the incremental pressure correction scheme. For each step in the pressure correction scheme, we derive a multimesh finite element formulation with suitable stabilization terms. The overall scheme yields expected spatial and temporal convergence rates on the Taylor-Green problem, and demonstrates good agreement for the drag and lift coefficients on the Turek-Schafer benchmark (DFG benchmark 2D-3). Finally, we illustrate the capabilities of the proposed scheme by optimizing the layout of obstacles in a channel.
Cite
@article{arxiv.1912.06392,
title = {A multimesh finite element method for the Navier-Stokes equations based on projection methods},
author = {Jørgen S. Dokken and August Johansson and André Massing and Simon W. Funke},
journal= {arXiv preprint arXiv:1912.06392},
year = {2020}
}