We present an overview of the most common numerical solution
strategies for the incompressible Navier–Stokes equations, including
fully implicit formulations, artificial compressibility methods, penalty
formulations, and operator splitting methods (pressure/velocity correction, projection methods). A unified framework that explains popular
operator splitting methods as special cases of a fully implicit approach
is also presented and can be used for constructing new and improved
solution strategies. The exposition is mostly neutral to the spatial
discretization technique, but we cover the need for staggered grids or
mixed finite elements and outline some alternative stabilization techniques that allow using standard grids. Emphasis is put on showing the close relationship between (seemingly) different and competing solution approaches for incompressible viscous flow.
%0 Journal Article
%1 langtangen2002numerical
%A Langtangen, Hans P.
%A Mardal, Kent-Andre
%A Winther, Ragnar
%D 2002
%J Advances in Water Resources
%K 76d05-incompressible-navier-stokes-equations 76m10-finite-element-methods-in-fluid-mechanics
%N 8-12
%P 1125--1146
%R 10.1016/s0309-1708(02)00052-0
%T Numerical Methods for Incompressible Viscous Flow
%U http://dx.doi.org/10.1016/s0309-1708(02)00052-0
%V 25
%X We present an overview of the most common numerical solution
strategies for the incompressible Navier–Stokes equations, including
fully implicit formulations, artificial compressibility methods, penalty
formulations, and operator splitting methods (pressure/velocity correction, projection methods). A unified framework that explains popular
operator splitting methods as special cases of a fully implicit approach
is also presented and can be used for constructing new and improved
solution strategies. The exposition is mostly neutral to the spatial
discretization technique, but we cover the need for staggered grids or
mixed finite elements and outline some alternative stabilization techniques that allow using standard grids. Emphasis is put on showing the close relationship between (seemingly) different and competing solution approaches for incompressible viscous flow.
@article{langtangen2002numerical,
abstract = {{We present an overview of the most common numerical solution
strategies for the incompressible Navier–Stokes equations, including
fully implicit formulations, artificial compressibility methods, penalty
formulations, and operator splitting methods (pressure/velocity correction, projection methods). A unified framework that explains popular
operator splitting methods as special cases of a fully implicit approach
is also presented and can be used for constructing new and improved
solution strategies. The exposition is mostly neutral to the spatial
discretization technique, but we cover the need for staggered grids or
mixed finite elements and outline some alternative stabilization techniques that allow using standard grids. Emphasis is put on showing the close relationship between (seemingly) different and competing solution approaches for incompressible viscous flow.}},
added-at = {2017-06-29T07:13:07.000+0200},
author = {Langtangen, Hans P. and Mardal, Kent-Andre and Winther, Ragnar},
biburl = {https://www.bibsonomy.org/bibtex/212f815b1420f70d80121213967a6d778/gdmcbain},
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citeulike-linkout-0 = {http://dx.doi.org/10.1016/s0309-1708(02)00052-0},
doi = {10.1016/s0309-1708(02)00052-0},
file = {langtangen_02_numerical_995944.pdf},
interhash = {3594ef41bbe3fdb65f610da04e28a70b},
intrahash = {12f815b1420f70d80121213967a6d778},
issn = {03091708},
journal = {Advances in Water Resources},
keywords = {76d05-incompressible-navier-stokes-equations 76m10-finite-element-methods-in-fluid-mechanics},
month = aug,
number = {8-12},
pages = {1125--1146},
posted-at = {2014-11-28 03:02:59},
priority = {5},
timestamp = {2020-05-27T03:36:13.000+0200},
title = {{Numerical Methods for Incompressible Viscous Flow}},
url = {http://dx.doi.org/10.1016/s0309-1708(02)00052-0},
volume = 25,
year = 2002
}