@Article{CiCP-22-494,
author = {Beaume , Cédric},
title = {Adaptive Stokes Preconditioning for Steady Incompressible Flows},
journal = {Communications in Computational Physics},
year = {2018},
volume = {22},
number = {2},
pages = {494--516},
abstract = {<p style="text-align: justify;">This paper describes an adaptive preconditioner for numerical continuation
of incompressible Navier–Stokes flows based on Stokes preconditioning [42] which
has been used successfully in studies of pattern formation in convection. The preconditioner
takes the form of the Helmholtz operator I−∆tL which maps the identity
(no preconditioner) for ∆t ≪ 1 to Laplacian preconditioning for ∆t ≫ 1. It is built on
a first order Euler time-discretization scheme and is part of the family of matrix-free
methods. The preconditioner is tested on two fluid configurations: three-dimensional
doubly diffusive convection and a two-dimensional projection of a shear flow. In the
former case, it is found that Stokes preconditioning is more efficient for ∆t = <span style="text-align: justify;">$\mathcal{O}$</span>(1),
away from the values used in the literature. In the latter case, the simple use of the
preconditioner is not sufficient and it is necessary to split the system of equations into
two subsystems which are solved simultaneously using two different preconditioners,
one of which is parameter dependent. Due to the nature of these applications and the
flexibility of the approach described, this preconditioner is expected to help in a wide
range of applications.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2016-0201},
url = {http://global-sci.org/intro/article_detail/cicp/11308.html}
}