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Investigation and application of point implicit Runge–Kutta methods to inviscid flow problems

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/
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:
AuthorsInstitution or Email of AuthorsAuthors ORCID iD
Langer, Stefanstefan.langer (at) dlr.deUNSPECIFIED
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:
EditorsEmail
Abgrall, RemyUNSPECIFIED
Farhat, CharbelUNSPECIFIED
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 Transport
DLR - Research area:Raumfahrt
DLR - Program:R RP - Raumtransport
DLR - Research theme (Project):R - Raumfahrzeugsysteme - Numerische Verfahren und Simulation
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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