Annals of Mathematical Sciences and Applications

Volume 5 (2020)

Number 1

Mathematical sciences related to theoretical physics, engineering, biology and economics

Guest Editor: Tony Wen-Hann Sheu, National Taiwan University

A pseudo-transient Newton–Krylov–Schwarz method for incompressible Navier–Stokes equations with slip conditions for bifurcation analysis

Pages: 41 – 61

DOI: https://dx.doi.org/10.4310/AMSA.2020.v5.n1.a2

Authors

Wen-Lieh Hsu (Department of Mathematics, National Central University, Taoyuan City, Taiwan)

Feng-Nan Hwang (Department of Mathematics, National Central University, Taoyuan City, Taiwan)

Abstract

We develop a parallel pseudo-transient Newton–Krylov–Schwarz ($\Psi$‑NKS) algorithm based on the Galerkin/least-squares finite element method for incompressible Navier–Stokes equations with slip boundary conditions. Many research works suggest that the slip condition can produce a more accurate numerical solution of fluid flow motion near the boundary for the case with a rough surface, porous media flows, and non-Newtonian flows. This study aims to investigate numerically how the slip condition affects the physical behavior of the fluid flows by using the $\Psi$‑NKS algorithm, including the flow structure of the lid-driven cavity and the critical Reynolds number for the pitchfork bifurcation of sudden expansion flows.

Keywords

incompressible Navier–Stokes equations, slip boundary conditions, domain decomposition method, Newton–Krylov–Schwarz algorithm, pitchfork bifurcation analysis

Full Text (PDF format)

Received 2 October 2019

Accepted 3 December 2019

Published 27 February 2020