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Preconditioned Newton methods to approximate solutions of the Reynolds averaged Navier-Stokes equations

Langer, Stefan (2018) Preconditioned Newton methods to approximate solutions of the Reynolds averaged Navier-Stokes equations. Habilitation. DLR-Forschungsbericht. DLR-FB-2018-19, 274 S. Deutschen Zentrum für Luft-und Raumfahrt.

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Abstract

We consider nonlinear agglomeration multigrid methods tailored to the efficient and robust solution of boundary value problems corresponding to the Reynolds averaged Navier-Stokes equations for the simulation of high Reynolds number turbulent flows. The presented solution algorithms are based on nonlinear agglomeration multigrid methods including implicit Runge-Kutta smoothers. The final formulation of these methods allows to interpret these smoothers as kinds of stabilized preconditioned Newton methods. The application of simplifications is used to derive almost all solution methods well known in the world of computational fluid dynamics. This hierarchy of methods gives insight in the potential and shortcomings of several established methods. To get a deeper understanding of the methods an analysis tool is suggested to evaluate certain smoothers. Several examples are presented to show the potential and shortcomings of certain methods derived in this thesis. Comparisons are done with respect to both robustness and efficiency of the scheme.

Item URL in elib:https://elib.dlr.de/121515/
Document Type:Monograph (DLR-Forschungsbericht, Habilitation)
Title:Preconditioned Newton methods to approximate solutions of the Reynolds averaged Navier-Stokes equations
Authors:
AuthorsInstitution or Email of AuthorsAuthors ORCID iD
Langer, StefanStefan.Langer (at) dlr.deUNSPECIFIED
Date:20 June 2018
Refereed publication:Yes
Open Access:Yes
Gold Open Access:No
In SCOPUS:No
In ISI Web of Science:No
Number of Pages:274
Publisher:Deutschen Zentrum für Luft-und Raumfahrt
ISSN:1434-8454
Status:Published
Keywords:RANS equations, preconditioned Newton method, nonlinear and linear multigrid, low Mach number flows, stability analysis
Institution:Institut für Aerodynamik und Strömungstechnik
Department:CASE
HGF - Research field:Aeronautics, Space and Transport
HGF - Program:Aeronautics
HGF - Program Themes:fixed-wing aircraft
DLR - Research area:Aeronautics
DLR - Program:L AR - Aircraft Research
DLR - Research theme (Project):L - VicToria
Location: Braunschweig
Institutes and Institutions:Institute for Aerodynamics and Flow Technology > CASE, BS
Deposited By: Langer, Dr.rer.nat. Stefan
Deposited On:11 Sep 2018 14:05
Last Modified:31 Jul 2019 20:19

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