Work

Nitsche method for Navier–Stokes equations with slip boundary conditions: convergence analysis and VMS-LES stabilization

Year: 2024

Type: article

Abstract: 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.

Source: ESAIM Mathematical Modelling and Numerical Analysis

DOI: 10.1051/m2an/2024070

Authors: Aparna Bansal, Nicolás A. Barnafi, Dwijendra Narain Pandey

Institutions: Indian Institute of Technology Roorkee, Centre National de la Recherche Scientifique, Pontificia Universidad Católica de Chile, Center for Mathematical Modeling

Language: English

Topic: Advanced Numerical Methods in Computational Mathematics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid:

Funders: Ministry of Education, India, Agencia Nacional de Investigación y Desarrollo