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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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author
; ; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
PAMM - Proceedings in Applied Mathematics and Mechanics
volume
16
pages
2 pages
publisher
John Wiley & Sons Inc.
conference name
Joint 87th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM) and Deutsche Mathematiker-Vereinigung (DMV), Braunschweig 2016
conference location
Braunschweig, Germany
conference dates
2016-03-07 - 2016-03-11
ISSN
1617-7061
DOI
10.1002/pamm.201610422
language
English
LU publication?
yes
additional info
Vol. 16 of PAMM is a special issue dedicated to the proceedings of the Joint 87th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM) and Deutsche Mathematiker-Vereinigung (DMV), Braunschweig 2016
id
03a6fd64-b61a-455b-a456-a7825ada089f
date added to LUP
2016-10-31 13:29:38
date last changed
2018-11-21 21:29:34
@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 Inc.}},
  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}},
  doi          = {{10.1002/pamm.201610422}},
  volume       = {{16}},
  year         = {{2016}},
}