Advanced

Preconditioned Smoothers for the Full Approximation Scheme for the RANS Equations

Birken, Philipp LU ; Bull, Jonathan and Jameson, Antony (2018) In Journal of Scientific Computing
Abstract

We consider multigrid methods for finite volume discretizations of the Reynolds averaged Navier–Stokes equations for both steady and unsteady flows. We analyze the effect of different smoothers based on pseudo time iterations, such as explicit and additive Runge–Kutta (AERK) methods. Furthermore, by deriving them from Rosenbrock smoothers, we identify some existing schemes as a class of additive W (AW) methods. This gives rise to two classes of preconditioned smoothers, preconditioned AERK and AW, which are implemented the exact same way, but have different parameters and properties. This derivation allows to choose some of these based on results for time integration methods. As preconditioners, we consider SGS preconditioners based on... (More)

We consider multigrid methods for finite volume discretizations of the Reynolds averaged Navier–Stokes equations for both steady and unsteady flows. We analyze the effect of different smoothers based on pseudo time iterations, such as explicit and additive Runge–Kutta (AERK) methods. Furthermore, by deriving them from Rosenbrock smoothers, we identify some existing schemes as a class of additive W (AW) methods. This gives rise to two classes of preconditioned smoothers, preconditioned AERK and AW, which are implemented the exact same way, but have different parameters and properties. This derivation allows to choose some of these based on results for time integration methods. As preconditioners, we consider SGS preconditioners based on flux vector splitting discretizations with a cutoff function for small eigenvalues. We compare these methods based on a discrete Fourier analysis. Numerical results on pitching and plunging airfoils identify AW3 as the best smoother regarding overall efficiency. Specifically, for the NACA 64A010 airfoil steady-state convergence rates of as low as 0.85 were achieved, or a reduction of 6 orders of magnitude in approximately 25 pseudo-time iterations. Unsteady convergence rates of as low as 0.77 were achieved, or a reduction of 11 orders of magnitude in approximately 70 pseudo-time iterations.

(Less)
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
epub
subject
keywords
Discrete Fourier analysis, Multigrid, Runge–Kutta smoothers, Unsteady flows
in
Journal of Scientific Computing
publisher
Springer
external identifiers
  • scopus:85051625285
ISSN
0885-7474
DOI
10.1007/s10915-018-0792-9
language
English
LU publication?
yes
id
2bfe496e-cbd3-44e0-b818-f3717d0c4675
date added to LUP
2018-09-13 10:53:48
date last changed
2019-01-14 07:39:56
@article{2bfe496e-cbd3-44e0-b818-f3717d0c4675,
  abstract     = {<p>We consider multigrid methods for finite volume discretizations of the Reynolds averaged Navier–Stokes equations for both steady and unsteady flows. We analyze the effect of different smoothers based on pseudo time iterations, such as explicit and additive Runge–Kutta (AERK) methods. Furthermore, by deriving them from Rosenbrock smoothers, we identify some existing schemes as a class of additive W (AW) methods. This gives rise to two classes of preconditioned smoothers, preconditioned AERK and AW, which are implemented the exact same way, but have different parameters and properties. This derivation allows to choose some of these based on results for time integration methods. As preconditioners, we consider SGS preconditioners based on flux vector splitting discretizations with a cutoff function for small eigenvalues. We compare these methods based on a discrete Fourier analysis. Numerical results on pitching and plunging airfoils identify AW3 as the best smoother regarding overall efficiency. Specifically, for the NACA 64A010 airfoil steady-state convergence rates of as low as 0.85 were achieved, or a reduction of 6 orders of magnitude in approximately 25 pseudo-time iterations. Unsteady convergence rates of as low as 0.77 were achieved, or a reduction of 11 orders of magnitude in approximately 70 pseudo-time iterations.</p>},
  author       = {Birken, Philipp and Bull, Jonathan and Jameson, Antony},
  issn         = {0885-7474},
  keyword      = {Discrete Fourier analysis,Multigrid,Runge–Kutta smoothers,Unsteady flows},
  language     = {eng},
  month        = {08},
  publisher    = {Springer},
  series       = {Journal of Scientific Computing},
  title        = {Preconditioned Smoothers for the Full Approximation Scheme for the RANS Equations},
  url          = {http://dx.doi.org/10.1007/s10915-018-0792-9},
  year         = {2018},
}