Stabilization and scalable block preconditioning for the Navier–Stokes equations

• Published in: Journal of computational physics Vol. 231; no. 2; pp. 345 - 363
• Main Authors: Cyr, Eric C., Shadid, John N., Tuminaro, Raymond S.
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Inc 2012; Elsevier
• Subjects: Block preconditioning; Computational techniques; Exact sciences and technology; Fully-implicit; Large-scale parallel; Mathematical methods in physics; Multilevel preconditioner; Navier–Stokes; Physics; Stabilized finite element; Multilevel preconditioner; Navier–Stokes; Stabilized finite element; Large-scale parallel; Block preconditioning; Fully-implicit; LU factorization; Stabilization; Decomposition method; Calculation methods; Discretization; Multigrid; Navier-Stokes; Calculation; Performance; Preconditioning; Navier-Stokes equations
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/j.jcp.2011.09.001

This study compares several block-oriented preconditioners for the stabilized finite element discretization of the incompressible Navier–Stokes equations. This includes standard additive Schwarz domain decomposition methods, aggressive coarsening multigrid, and three preconditioners based on an approximate block LU factorization, specifically SIMPLEC, LSC, and PCD. Robustness is considered with a particular focus on the impact that different stabilization methods have on preconditioner performance. Additionally, parallel scaling studies are undertaken. The numerical results indicate that aggressive coarsening multigrid, LSC and PCD all have good algorithmic scalability. Coupling this with the fact that block methods can be applied to systems arising from stable mixed discretizations implies that these techniques are a promising direction for developing scalable methods for Navier–Stokes.