| Issue |
ESAIM: M2AN
Volume 58, Number 5, September-October 2024
|
|
|---|---|---|
| Page(s) | 2079 - 2115 | |
| DOI | https://doi.org/10.1051/m2an/2024070 | |
| Published online | 21 October 2024 | |
Nitsche method for Navier–Stokes equations with slip boundary conditions: convergence analysis and VMS-LES stabilization
1
Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee 247667, India
2
Instituto de Ingeniería Matemática y Computacional & Facultad de Ciencias Biológicas, Pontificia Universidad Católica de Chile, Av. Vicuña Mackenna, 4860 Santiago, Chile
3
Centro de Modelamiento Matemático (CNRS IRL2807), Santiago, Chile
* Corresponding author: dwijpfma@iitr.ac.in
Received:
12
August
2023
Accepted:
5
September
2024
In this paper, we analyze Nitsche’s method for the stationary Navier–Stokes equations on Lipschitz domains under minimal regularity assumptions. Our analysis provides a robust formulation for implementing slip (i.e., Navier) boundary conditions in arbitrarily complex boundaries. The well-posedness of the discrete problem is established using the Banach Nečas–Babuška and Banach fixed point theorems under standard small data assumptions. We also provide optimal convergence rates for the approximation error. Furthermore, we propose a quasi-static VMS-LES formulation with Nitsche for the Navier–Stokes equations with slip boundary conditions to address the simulation of incompressible fluids at high Reynolds numbers. We validate our theory through several numerical tests in well-established benchmark problems.
Mathematics Subject Classification: 65N30 / 65N12 / 65N15 / 65J15 / 76D07
Key words: Navier–Stokes equations / Navier boundary conditions / Nitsche’s method / Banach fixed point theorem / Banach–Nečas–Babuška theorem / a priori analysis / variational multiscale modeling / large eddy simulation
© The authors. Published by EDP Sciences, SMAI 2024
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