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A comparison of Rosenbrock and ESDIRK methods combined with iterative solvers for unsteady compressible flows

Blom, David S.; Birken, Philipp LU ; Bijl, Hester; Kessels, Fleur; Meister, Andreas and van Zuijlen, Alexander H. (2016) In Advances in Computational Mathematics
Abstract
In this article, we endeavour to find a fast solver for finite volume discretizations for compressible unsteady viscous flows. Thereby, we concentrate on comparing the efficiency of important classes of time integration schemes, namely time adaptive Rosenbrock, singly diagonally implicit (SDIRK) and explicit first stage singly diagonally implicit Runge-Kutta (ESDIRK) methods. To make the comparison fair, efficient equation system solvers need to be chosen and a smart choice of tolerances is needed. This is determined from the tolerance TOL that steers time adaptivity. For implicit Runge-Kutta methods, the solver is given by preconditioned inexact Jacobian-free Newton-Krylov (JFNK) and for Rosenbrock, it is preconditioned Jacobian-free... (More)
In this article, we endeavour to find a fast solver for finite volume discretizations for compressible unsteady viscous flows. Thereby, we concentrate on comparing the efficiency of important classes of time integration schemes, namely time adaptive Rosenbrock, singly diagonally implicit (SDIRK) and explicit first stage singly diagonally implicit Runge-Kutta (ESDIRK) methods. To make the comparison fair, efficient equation system solvers need to be chosen and a smart choice of tolerances is needed. This is determined from the tolerance TOL that steers time adaptivity. For implicit Runge-Kutta methods, the solver is given by preconditioned inexact Jacobian-free Newton-Krylov (JFNK) and for Rosenbrock, it is preconditioned Jacobian-free GMRES. To specify the tolerances in there, we suggest a simple strategy of using TOL/100 that is a good compromise between stability and computational effort. Numerical experiments for different test cases show that the fourth order Rosenbrock method RODASP and the fourth order ESDIRK method ESDIRK4 are best for fine tolerances, with RODASP being the most robust scheme. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
epub
subject
keywords
Rosenbrock methods, Navier-Stokes equations, ESDIRK, Jacobian-free Newton-Krylov, Unsteady flows, Time adaptivity
in
Advances in Computational Mathematics
pages
26 pages
publisher
Springer
external identifiers
  • Scopus:84978032472
ISSN
1572-9044
DOI
10.1007/s10444-016-9468-x
language
English
LU publication?
yes
id
046e2540-68a0-4ba8-bddc-2f88ba9f79e4
date added to LUP
2016-06-23 11:17:08
date last changed
2016-11-01 08:15:58
@misc{046e2540-68a0-4ba8-bddc-2f88ba9f79e4,
  abstract     = {In this article, we endeavour to find a fast solver for finite volume discretizations for compressible unsteady viscous flows. Thereby, we concentrate on comparing the efficiency of important classes of time integration schemes, namely time adaptive Rosenbrock, singly diagonally implicit (SDIRK) and explicit first stage singly diagonally implicit Runge-Kutta (ESDIRK) methods. To make the comparison fair, efficient equation system solvers need to be chosen and a smart choice of tolerances is needed. This is determined from the tolerance TOL that steers time adaptivity. For implicit Runge-Kutta methods, the solver is given by preconditioned inexact Jacobian-free Newton-Krylov (JFNK) and for Rosenbrock, it is preconditioned Jacobian-free GMRES. To specify the tolerances in there, we suggest a simple strategy of using TOL/100 that is a good compromise between stability and computational effort. Numerical experiments for different test cases show that the fourth order Rosenbrock method RODASP and the fourth order ESDIRK method ESDIRK4 are best for fine tolerances, with RODASP being the most robust scheme.},
  author       = {Blom, David S. and Birken, Philipp and Bijl, Hester and Kessels, Fleur and Meister, Andreas and van Zuijlen, Alexander H.},
  issn         = {1572-9044},
  keyword      = {Rosenbrock methods,Navier-Stokes equations,ESDIRK,Jacobian-free Newton-Krylov,Unsteady flows,Time adaptivity},
  language     = {eng},
  month        = {06},
  pages        = {26},
  publisher    = {ARRAY(0xa3d5ef0)},
  series       = {Advances in Computational Mathematics},
  title        = {A comparison of Rosenbrock and ESDIRK methods combined with iterative solvers for unsteady compressible flows},
  url          = {http://dx.doi.org/10.1007/s10444-016-9468-x},
  year         = {2016},
}