Stability and convergence of efficient Navier-Stokes solvers via a commutator estimate


Journal Article

For strong solutions of the incompressible Navier-Stokes equations in bounded domains with velocity specified at the boundary, we establish the unconditional stability and convergence of discretization schemes that decouple the updates of pressure and velocity through explicit time stepping for pressure. These schemes require no solution of stationary Stokes systems, nor any compatibility between velocity and pressure spaces to ensure an inf-sup condition, and are representative of a class of highly efficient computational methods that have recently emerged. The proofs are simple, based upon a new, sharp estimate for the commutator of the Laplacian and Helmholtz projection operators. This allows us to treat an unconstrained formulation of the Navier-Stokes equations as a perturbed diffusion equation. ©2006 Wiley Periodicals, Inc.

Full Text

Duke Authors

Cited Authors

  • Liu, JG; Liu, J; Pego, RL

Published Date

  • October 1, 2007

Published In

Volume / Issue

  • 60 / 10

Start / End Page

  • 1443 - 1487

Electronic International Standard Serial Number (EISSN)

  • 0010-3640

International Standard Serial Number (ISSN)

  • 0010-3640

Digital Object Identifier (DOI)

  • 10.1002/cpa.20178

Citation Source

  • Scopus