A Simplified Parallel Two-Level Iterative Method for Simulation of Incompressible Navier-Stokes Equations (Advances in Applied Mathematics and Mechanics, 2021)
Based on two-grid discretization, a simplified parallel iterative finite elementmethod for the simulation of incompressible Navier-Stokes equations is developedand analyzed. The method is based on a fixed point iteration for the equations ona coarse grid, where a Stokes problem is solved at each iteration. Then, on overlappedlocal fine grids, corrections are calculated in parallel by solving an Oseen problem inwhich the fixed convection is given by the coarse grid solution. Error bounds of theapproximate solution are derived. Numerical results on examples of known analyticalsolutions, lid-driven cavity flow and backward-facing step flow are also given todemonstrate the effectiveness of the method.