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Efficient Time Integration of IMEX Type using Exponential Integrators for Compressible, Viscous Flow Simulation

Veronika, Straub; Ortleb, Sigrun; Birken, Philipp LU and Meister, Andreas (2016) Joint 87th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM) and Deutsche Mathematiker-Vereinigung (DMV), Braunschweig 2016 In PAMM - Proceedings in Applied Mathematics and Mechanics 16. p.867-868
Abstract
We investigate the adaption of the recently developed exponential integrators called EPIRK in the so-called domain-based implicit-explicit (IMEX) setting of spatially discretized PDE's. The EPIRK schemes were shown to be efficient for sufficiently stiff problems and offer high precision and good stability properties like A- and L-stability in theory. In practice, however, we can show that these stability properties are dependent on the parameters of the interior approximation techniques.

Here, we introduce the IMEX-EPIRK method, which consists of coupling an explicit Runge-Kutta scheme with an EPIRK scheme. We briefly analyze its linear stability, show its conservation property and set up a CFL condition. Though the method is... (More)
We investigate the adaption of the recently developed exponential integrators called EPIRK in the so-called domain-based implicit-explicit (IMEX) setting of spatially discretized PDE's. The EPIRK schemes were shown to be efficient for sufficiently stiff problems and offer high precision and good stability properties like A- and L-stability in theory. In practice, however, we can show that these stability properties are dependent on the parameters of the interior approximation techniques.

Here, we introduce the IMEX-EPIRK method, which consists of coupling an explicit Runge-Kutta scheme with an EPIRK scheme. We briefly analyze its linear stability, show its conservation property and set up a CFL condition. Though the method is convergent of only first order, it demonstrates the advantages of this novel type of schemes for stiff problems very well. (Less)
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organization
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Contribution to journal
publication status
published
subject
in
PAMM - Proceedings in Applied Mathematics and Mechanics
volume
16
pages
2 pages
publisher
John Wiley & Sons
conference name
Joint 87th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM) and Deutsche Mathematiker-Vereinigung (DMV), Braunschweig 2016
ISSN
1617-7061
DOI
10.1002/pamm.201610422
language
English
LU publication?
yes
id
03a6fd64-b61a-455b-a456-a7825ada089f
date added to LUP
2016-10-31 13:29:38
date last changed
2017-02-16 12:55:20
@article{03a6fd64-b61a-455b-a456-a7825ada089f,
  abstract     = {We investigate the adaption of the recently developed exponential integrators called EPIRK in the so-called domain-based implicit-explicit (IMEX) setting of spatially discretized PDE's. The EPIRK schemes were shown to be efficient for sufficiently stiff problems and offer high precision and good stability properties like A- and L-stability in theory. In practice, however, we can show that these stability properties are dependent on the parameters of the interior approximation techniques.<br/><br/>Here, we introduce the IMEX-EPIRK method, which consists of coupling an explicit Runge-Kutta scheme with an EPIRK scheme. We briefly analyze its linear stability, show its conservation property and set up a CFL condition. Though the method is convergent of only first order, it demonstrates the advantages of this novel type of schemes for stiff problems very well.},
  author       = {Veronika, Straub and Ortleb, Sigrun and Birken, Philipp and Meister, Andreas},
  issn         = {1617-7061},
  language     = {eng},
  month        = {10},
  pages        = {867--868},
  publisher    = {John Wiley & Sons},
  series       = {PAMM - Proceedings in Applied Mathematics and Mechanics},
  title        = {Efficient Time Integration of IMEX Type using Exponential Integrators for Compressible, Viscous Flow Simulation},
  url          = {http://dx.doi.org/10.1002/pamm.201610422},
  volume       = {16},
  year         = {2016},
}