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Solving nonlinear systems inside implicit time integration schemes for unsteady viscous flows

Birken, P. LU (2013) Recent Developments in the Numerics of Nonlinear Hyperbolic Conservation Laws and their Use in Science and Engineering In Notes on Numerical Fluid Mechanics and Multidisciplinary Design 120. p.57-71
Abstract
We considered nonlinear solvers inside implicit time integration schemes for the time dependent compressible Navier-Stokes equations. The existing solvers turn out to be adequate, but amenable to significant improvements. Regarding multigrid schemes, we demonstrated that reoptimizing a multigrid scheme for the case of a time dependent equation leads to significant improvements in convergence speed compared to reusing the steady state method. As for Newton schemes, inexact Jacobian-free Newton-GMRES methods using the Eisenstat-Walker strategy are easy to implement and fast and, as opposed to the situation for steady flows, a true alternative to multigrid.
Please use this url to cite or link to this publication:
author
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
host publication
Recent Developments in the Numerics of Nonlinear Hyperbolic Conservation Laws : Lectures Presented at a Workshop at the Mathematical Research Institute Oberwolfach, Germany, Jan 15 – 21, 2012 - Lectures Presented at a Workshop at the Mathematical Research Institute Oberwolfach, Germany, Jan 15 – 21, 2012
series title
Notes on Numerical Fluid Mechanics and Multidisciplinary Design
editor
Ansorge, Rainer ; Bijl, Hester ; Meister, Andreas and Sonar, Thomas
volume
120
pages
57 - 71
publisher
Springer
conference name
Recent Developments in the Numerics of Nonlinear Hyperbolic Conservation Laws and their Use in Science and Engineering
conference location
Oberwolfach, Germany
conference dates
2012-01-15 - 2012-01-21
external identifiers
  • scopus:84868562237
ISSN
1860-0824
1612-2909
ISBN
9783642332203
9783642332210
DOI
10.1007/978-3-642-33221-0_4
language
English
LU publication?
no
id
55817393-ef2c-4df1-949e-743fcd7b7b58
date added to LUP
2019-02-08 11:24:01
date last changed
2024-03-19 01:17:16
@inproceedings{55817393-ef2c-4df1-949e-743fcd7b7b58,
  abstract     = {{We considered nonlinear solvers inside implicit time integration schemes for the time dependent compressible Navier-Stokes equations. The existing solvers turn out to be adequate, but amenable to significant improvements. Regarding multigrid schemes, we demonstrated that reoptimizing a multigrid scheme for the case of a time dependent equation leads to significant improvements in convergence speed compared to reusing the steady state method. As for Newton schemes, inexact Jacobian-free Newton-GMRES methods using the Eisenstat-Walker strategy are easy to implement and fast and, as opposed to the situation for steady flows, a true alternative to multigrid.}},
  author       = {{Birken, P.}},
  booktitle    = {{Recent Developments in the Numerics of Nonlinear Hyperbolic Conservation Laws : Lectures Presented at a Workshop at the Mathematical Research Institute Oberwolfach, Germany, Jan 15 – 21, 2012}},
  editor       = {{Ansorge, Rainer and Bijl, Hester and Meister, Andreas and Sonar, Thomas}},
  isbn         = {{9783642332203}},
  issn         = {{1860-0824}},
  language     = {{eng}},
  pages        = {{57--71}},
  publisher    = {{Springer}},
  series       = {{Notes on Numerical Fluid Mechanics and Multidisciplinary Design}},
  title        = {{Solving nonlinear systems inside implicit time integration schemes for unsteady viscous flows}},
  url          = {{http://dx.doi.org/10.1007/978-3-642-33221-0_4}},
  doi          = {{10.1007/978-3-642-33221-0_4}},
  volume       = {{120}},
  year         = {{2013}},
}