This paper describes an adaptive preconditioner for numerical continuation of
incompressible Navier--Stokes flows. The preconditioner maps the identity (no
preconditioner) to the Stokes preconditioner (preconditioning by Laplacian)
through a continuous parameter and is built on a first order Euler
time-discretization scheme. The preconditioner is tested onto two fluid
configurations: three-dimensional doubly diffusive convection and a reduced
model of shear flows. In the former case, Stokes preconditioning works but a
mixed preconditioner is preferred. In the latter case, the system of equation
is split and solved simultaneously using two different preconditioners, one of
which is parameter dependent. Due to the nature of these applications, this
preconditioner is expected to help a wide range of studies.
%0 Journal Article
%1 Beaume2016Adaptive
%A Beaume, Cédric
%D 2016
%J Communications in Computational Physics
%K 35b60-pdes-continuation-and-prolongation-of-solutions 35q30-navier-stokes-equations 65f08-preconditioners-for-iterative-methods 65h20-global-methods-including-homotopy-approaches 76d05-incompressible-navier-stokes-equations 76r50-diffusion
%N 02
%P 494--516
%R 10.4208/cicp.oa-2016-0201
%T An Adaptive Preconditioner for Steady Incompressible Flows
%U http://dx.doi.org/10.4208/cicp.oa-2016-0201
%V 22
%X This paper describes an adaptive preconditioner for numerical continuation of
incompressible Navier--Stokes flows. The preconditioner maps the identity (no
preconditioner) to the Stokes preconditioner (preconditioning by Laplacian)
through a continuous parameter and is built on a first order Euler
time-discretization scheme. The preconditioner is tested onto two fluid
configurations: three-dimensional doubly diffusive convection and a reduced
model of shear flows. In the former case, Stokes preconditioning works but a
mixed preconditioner is preferred. In the latter case, the system of equation
is split and solved simultaneously using two different preconditioners, one of
which is parameter dependent. Due to the nature of these applications, this
preconditioner is expected to help a wide range of studies.
@article{Beaume2016Adaptive,
abstract = {{This paper describes an adaptive preconditioner for numerical continuation of
incompressible Navier--Stokes flows. The preconditioner maps the identity (no
preconditioner) to the Stokes preconditioner (preconditioning by Laplacian)
through a continuous parameter and is built on a first order Euler
time-discretization scheme. The preconditioner is tested onto two fluid
configurations: three-dimensional doubly diffusive convection and a reduced
model of shear flows. In the former case, Stokes preconditioning works but a
mixed preconditioner is preferred. In the latter case, the system of equation
is split and solved simultaneously using two different preconditioners, one of
which is parameter dependent. Due to the nature of these applications, this
preconditioner is expected to help a wide range of studies.}},
added-at = {2019-03-01T00:11:50.000+0100},
archiveprefix = {arXiv},
author = {Beaume, C\'{e}dric},
biburl = {https://www.bibsonomy.org/bibtex/210187e694fe664033ce1de1e008f5d7b/gdmcbain},
citeulike-article-id = {14414542},
citeulike-linkout-0 = {http://arxiv.org/abs/1604.04532},
citeulike-linkout-1 = {http://arxiv.org/pdf/1604.04532},
citeulike-linkout-2 = {http://dx.doi.org/10.4208/cicp.oa-2016-0201},
day = 14,
doi = {10.4208/cicp.oa-2016-0201},
eprint = {1604.04532},
interhash = {3d391b7675bf7b4cbc1017b3b46c6157},
intrahash = {10187e694fe664033ce1de1e008f5d7b},
issn = {1815-2406},
journal = {Communications in Computational Physics},
keywords = {35b60-pdes-continuation-and-prolongation-of-solutions 35q30-navier-stokes-equations 65f08-preconditioners-for-iterative-methods 65h20-global-methods-including-homotopy-approaches 76d05-incompressible-navier-stokes-equations 76r50-diffusion},
month = apr,
number = 02,
pages = {494--516},
posted-at = {2017-08-16 04:17:59},
priority = {2},
timestamp = {2019-03-01T00:11:50.000+0100},
title = {{An Adaptive Preconditioner for Steady Incompressible Flows}},
url = {http://dx.doi.org/10.4208/cicp.oa-2016-0201},
volume = 22,
year = 2016
}