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

We develop a parallel pseudo-transient Newton-Krylov-Schwarz (Ψ-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 Ψ-NKS algorithm, including the flow structure of the lid-driven cavity and the critical Reynolds number for the pitchfork bifurcation of sudden expansion flows.