Stabilized bi-grid projection methods in Finite Elements for the 2D incompressible Navier-Stokes
For computational fluid dynamics researchers, this provides a more efficient finite element solver for incompressible flows, though it is an incremental improvement over existing projection methods.
The paper introduces bi-grid projection methods for 2D incompressible Navier-Stokes equations that combine implicit coarse-grid and stabilized semi-implicit fine-grid computations, achieving enhanced stability up to Re=7500 and significant CPU time savings compared to implicit projection schemes.
We introduce a family of bi-grid schemes in finite elements for solving 2D incompressible Navier-Stokes equations in velocity and pressure $(u,p)$. The new schemes are based on projection methods and use two pairs of FEM spaces, a sparse and a fine one. The main computational effort is done on the coarsest velocity space with an implicit and unconditionally time scheme while its correction on the finer velocity space is realized with a simple stabilized semi-implicit scheme whose the lack of stability is compensated by a high mode stabilization procedure; the pressure is updated using the free divergence property. The new schemes are tested on the lid driven cavity up to $Re=7500$. An enhanced stability is observed as respect to classical semi-implicit methods and an important gain of CPU time is obtained as compared to implicit projection schemes.