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A STUDY of multigrid smoothers used in compressible CFD based on the convection diffusion equation

Birken, Philipp LU ; Bull, Jonathan and Jameson, Antony (2016) 7th European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS Congress 2016 In ECCOMAS Congress 2016 - Proceedings of the 7th European Congress on Computational Methods in Applied Sciences and Engineering 2. p.2648-2663
Abstract

We look at multigrid methods for unsteady viscous compressible flows. We specifically target smoothers that can be used in parallel and without computation of a Jacobian, which are particlarly attractive candidates in the context of Discontinuous Galerkin discretizations. In CFD, a plethora of nonlinear smoothers have been suggested which are hard to analyze. Our methodology is to use a linear model problem, here the convection diffusion equation, to be able to classify and compare smoothers better. Specifically, we consider explicit and implicit pseudo time iterations, GMRES as a smoother, SGS and implicit line smoothers. We relate GMRES to explicit Runge-Kutta smoothers, identify implicit line smoothers as Block Jacobi and analyze the... (More)

We look at multigrid methods for unsteady viscous compressible flows. We specifically target smoothers that can be used in parallel and without computation of a Jacobian, which are particlarly attractive candidates in the context of Discontinuous Galerkin discretizations. In CFD, a plethora of nonlinear smoothers have been suggested which are hard to analyze. Our methodology is to use a linear model problem, here the convection diffusion equation, to be able to classify and compare smoothers better. Specifically, we consider explicit and implicit pseudo time iterations, GMRES as a smoother, SGS and implicit line smoothers. We relate GMRES to explicit Runge-Kutta smoothers, identify implicit line smoothers as Block Jacobi and analyze the potential of implicit pseudo time iterations. Finally, we discuss the relation between methods for steady and unsteady flows. Numerical results show that GMRES is a very attractive smoother in this context.

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author
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
keywords
Multigrid, Unsteady flows
in
ECCOMAS Congress 2016 - Proceedings of the 7th European Congress on Computational Methods in Applied Sciences and Engineering
volume
2
pages
16 pages
publisher
National Technical University of Athens
conference name
7th European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS Congress 2016
external identifiers
  • scopus:84995445029
ISBN
9786188284401
language
English
LU publication?
yes
id
f1091b45-491e-4845-9476-4c4e03029466
date added to LUP
2017-02-23 14:10:23
date last changed
2017-05-16 13:42:32
@inproceedings{f1091b45-491e-4845-9476-4c4e03029466,
  abstract     = {<p>We look at multigrid methods for unsteady viscous compressible flows. We specifically target smoothers that can be used in parallel and without computation of a Jacobian, which are particlarly attractive candidates in the context of Discontinuous Galerkin discretizations. In CFD, a plethora of nonlinear smoothers have been suggested which are hard to analyze. Our methodology is to use a linear model problem, here the convection diffusion equation, to be able to classify and compare smoothers better. Specifically, we consider explicit and implicit pseudo time iterations, GMRES as a smoother, SGS and implicit line smoothers. We relate GMRES to explicit Runge-Kutta smoothers, identify implicit line smoothers as Block Jacobi and analyze the potential of implicit pseudo time iterations. Finally, we discuss the relation between methods for steady and unsteady flows. Numerical results show that GMRES is a very attractive smoother in this context.</p>},
  author       = {Birken, Philipp and Bull, Jonathan and Jameson, Antony},
  booktitle    = {ECCOMAS Congress 2016 - Proceedings of the 7th European Congress on Computational Methods in Applied Sciences and Engineering},
  isbn         = {9786188284401},
  keyword      = {Multigrid,Unsteady flows},
  language     = {eng},
  pages        = {2648--2663},
  publisher    = {National Technical University of Athens},
  title        = {A STUDY of multigrid smoothers used in compressible CFD based on the convection diffusion equation},
  volume       = {2},
  year         = {2016},
}