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Isogeometric Analysis on Multiple Patches for Aerospace Applications

Rusch, Thorben Konstantin (2018) Isogeometric Analysis on Multiple Patches for Aerospace Applications. Bachelor's, Institut für Simulations- und Softwaretechnik.

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Abstract

Computer-driven simulations in the context of aerospace research are of paramount importance. These simulations are done by solving partial differential equations approximately with numerical methods. One famous and recent approach in this context is the isogeometric analysis (IGA) which is able to simulate directly on smooth geometries. Since in most real-world applications the geometries are given as CAD files, the isogeometric approach has to be extended to more complicated geometries, i.e. NURBS-based multiple patches. The contributions of this thesis are that we derive an isogeometric method on multiple patches. Since this a restricted variational problem for elliptic equations, we solve it with the generalized Lagrange multipliers method. Furthermore, we give an estimation for the integration complexity of IGA and compare it to the integration complexity of the classical finite element method (FEM). We demonstrate that the a-priori error of IGA on single patches is the same as encountered in the a-priori error analysis of FEM. In addition, we show that the condition number of IGA increases exponentially with increasing polynomial degree and that it is asymptotically of the same order as the condition number of FEM under h-refinement. Finally, we simulate a potential flow around a NACA airfoil in two dimensions using the isogeometric method on multiple patches. This provides information about the problems and challenges in the application of IGA in modern aerospace science.

Item URL in elib:https://elib.dlr.de/124101/
Document Type:Thesis (Bachelor's)
Additional Information:Betreuer: Dr. Martin Siggel
Title:Isogeometric Analysis on Multiple Patches for Aerospace Applications
Authors:
AuthorsInstitution or Email of AuthorsAuthors ORCID iD
Rusch, Thorben Konstantinkonstantin.rusch (at) dlr.deUNSPECIFIED
Date:April 2018
Refereed publication:Yes
Open Access:Yes
Gold Open Access:No
In SCOPUS:No
In ISI Web of Science:No
Number of Pages:44
Status:Unpublished
Keywords:Isogeometric Analysis Partial Differential Equations h,p,k-FEM NURBS B-Splines
Institution:Institut für Simulations- und Softwaretechnik
Department:High Performance Computing
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, R - Vorhaben SISTEC
Location: Köln-Porz
Institutes and Institutions:Institut of Simulation and Software Technology > High Performance Computing
Deposited By: Rusch, Konstantin
Deposited On:03 Dec 2018 18:05
Last Modified:31 Jul 2019 20:21

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