Langer, Stefan (2012) Investigation and application of point implicit Runge–Kutta methods to inviscid flow problems. International Journal for Numerical Methods in Fluids, 69 (2), pp. 332-352. Wiley. doi: DOI: 10.1002/fld.2561. ISSN 0271-2091.
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Abstract
We derive and investigate point implicit Runge–Kutta methods to significantly improve the convergence rate to approximate steady-state solutions of inviscid flows. It turns out that the point implicit Runge–Kutta can be interpreted as a preconditioned explicit Runge–Kutta method, where the preconditioner arises naturally as local derivative of the residual function. Moreover, many preconditioners suggested in the literature so far are identified as special case of our general ansatz. Conditions will be formulated such that explicit Runge–Kutta methods with local time stepping are equivalent to point implicit methods. In numerical examples, we will demonstrate the improved convergence rates.
Item URL in elib: | https://elib.dlr.de/72688/ | |||||||||
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Document Type: | Article | |||||||||
Additional Information: | Published online: 29. APR 2011 | |||||||||
Title: | Investigation and application of point implicit Runge–Kutta methods to inviscid flow problems | |||||||||
Authors: |
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Date: | 2012 | |||||||||
Journal or Publication Title: | International Journal for Numerical Methods in Fluids | |||||||||
Refereed publication: | Yes | |||||||||
Open Access: | No | |||||||||
Gold Open Access: | No | |||||||||
In SCOPUS: | Yes | |||||||||
In ISI Web of Science: | Yes | |||||||||
Volume: | 69 | |||||||||
DOI: | DOI: 10.1002/fld.2561 | |||||||||
Page Range: | pp. 332-352 | |||||||||
Editors: |
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Publisher: | Wiley | |||||||||
ISSN: | 0271-2091 | |||||||||
Status: | Published | |||||||||
Keywords: | Runge–Kutta methods; point implicit; local time stepping; matrix dissipation; inviscid flow problem; multigrid | |||||||||
HGF - Research field: | Aeronautics, Space and Transport | |||||||||
HGF - Program: | Space | |||||||||
HGF - Program Themes: | Space Transportation | |||||||||
DLR - Research area: | Raumfahrt | |||||||||
DLR - Program: | R RP - Space Transportation | |||||||||
DLR - Research theme (Project): | R - Raumfahrzeugsysteme - Numerische Verfahren und Simulation (old) | |||||||||
Location: | Braunschweig | |||||||||
Institutes and Institutions: | Institute of Aerodynamics and Flow Technology > C²A²S²E - Center for Computer Applications in AeroSpace Science and Engineering | |||||||||
Deposited By: | Langer, Dr.rer.nat. Stefan | |||||||||
Deposited On: | 12 Dec 2011 15:55 | |||||||||
Last Modified: | 08 Mar 2018 18:37 |
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