Research article

Stabilized bi-grid projection methods in finite elements for the 2D incompressible Navier-Stokes equations

  • Received: 28 August 2018 Accepted: 18 October 2018 Published: 29 October 2018
  • 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 e ort 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.

    Citation: Hyam Abboud, Clara Al Kosseifi, Jean-Paul Chehab. Stabilized bi-grid projection methods in finite elements for the 2D incompressible Navier-Stokes equations[J]. AIMS Mathematics, 2018, 3(4): 485-513. doi: 10.3934/Math.2018.4.485

    Related Papers:

  • 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 e ort 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.


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