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

P. Birken

doi:10.1007/978-3-642-33221-0_4

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

P. Birken

University of Kassel

Research output: Chapter in Book/Report/Conference proceeding › Paper in conference proceeding › peer-review

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.

Original language	English
Title of host publication	Recent Developments in the Numerics of Nonlinear Hyperbolic Conservation Laws
Subtitle of host publication	Lectures Presented at a Workshop at the Mathematical Research Institute Oberwolfach, Germany, Jan 15 – 21, 2012
Editors	Rainer Ansorge, Hester Bijl, Andreas Meister, Thomas Sonar
Publisher	Springer
Pages	57-71
ISBN (Electronic)	9783642332210
ISBN (Print)	9783642332203
DOIs	https://doi.org/10.1007/978-3-642-33221-0_4
Publication status	Published - 2013
Externally published	Yes
Event	Recent Developments in the Numerics of Nonlinear Hyperbolic Conservation Laws and their Use in Science and Engineering - Oberwolfach, Germany Duration: 2012 Jan 15 → 2012 Jan 21

Publication series

Name	Notes on Numerical Fluid Mechanics and Multidisciplinary Design
Publisher	Springer
Volume	120
ISSN (Print)	1612-2909
ISSN (Electronic)	1860-0824

Workshop

Workshop	Recent Developments in the Numerics of Nonlinear Hyperbolic Conservation Laws and their Use in Science and Engineering
Country/Territory	Germany
City	Oberwolfach
Period	2012/01/15 → 2012/01/21

Subject classification (UKÄ)

Fluid Mechanics and Acoustics

Access to Document

10.1007/978-3-642-33221-0_4

Cite this

Birken, P. (2013). Solving nonlinear systems inside implicit time integration schemes for unsteady viscous flows. In R. Ansorge, H. Bijl, A. Meister, & T. Sonar (Eds.), 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 (pp. 57-71). (Notes on Numerical Fluid Mechanics and Multidisciplinary Design; Vol. 120). Springer. https://doi.org/10.1007/978-3-642-33221-0_4

Birken, P. / Solving nonlinear systems inside implicit time integration schemes for unsteady viscous flows. 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 / Rainer Ansorge ; Hester Bijl ; Andreas Meister ; Thomas Sonar. Springer, 2013. pp. 57-71 (Notes on Numerical Fluid Mechanics and Multidisciplinary Design).

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title = "Solving nonlinear systems inside implicit time integration schemes for unsteady viscous flows",

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 = "P. Birken",

year = "2013",

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isbn = "9783642332203",

series = "Notes on Numerical Fluid Mechanics and Multidisciplinary Design",

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editor = "Rainer Ansorge and Hester Bijl and Andreas Meister and Thomas Sonar",

booktitle = "Recent Developments in the Numerics of Nonlinear Hyperbolic Conservation Laws",

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Birken, P 2013, Solving nonlinear systems inside implicit time integration schemes for unsteady viscous flows. in R Ansorge, H Bijl, A Meister & T Sonar (eds), 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. Notes on Numerical Fluid Mechanics and Multidisciplinary Design, vol. 120, Springer, pp. 57-71, Recent Developments in the Numerics of Nonlinear Hyperbolic Conservation Laws and their Use in Science and Engineering, Oberwolfach, Germany, 2012/01/15. https://doi.org/10.1007/978-3-642-33221-0_4

Solving nonlinear systems inside implicit time integration schemes for unsteady viscous flows. / Birken, P.
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. ed. / Rainer Ansorge; Hester Bijl; Andreas Meister; Thomas Sonar. Springer, 2013. p. 57-71 (Notes on Numerical Fluid Mechanics and Multidisciplinary Design; Vol. 120).

Research output: Chapter in Book/Report/Conference proceeding › Paper in conference proceeding › peer-review

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N2 - 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.

AB - 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.

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Birken P. Solving nonlinear systems inside implicit time integration schemes for unsteady viscous flows. In Ansorge R, Bijl H, Meister A, Sonar T, editors, 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. Springer. 2013. p. 57-71. (Notes on Numerical Fluid Mechanics and Multidisciplinary Design). doi: 10.1007/978-3-642-33221-0_4

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

Abstract

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Workshop

Subject classification (UKÄ)

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Cite this