 | Franz T. Reduced-order modeling for steady transonic flows via manifold learning: Diss. … Dr.-Ing. / Deutsches Zentrum für Luft- und Raumfahrt, Institut für Aerodynamik und Strömungstechnik, Braunschweig. - Köln: DLR, 2016. - xv, 114 p.: ill., tab. - (Forschungsbericht; 2016-14). - Res. also Germ. - Bibliogr.: p.107-114. - ISSN 1434-8454
Шифр: (Pr 1120/2016-14) 02
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Acronyms ....................................................... xi
Notations .................................................... xiii
1 Introduction ................................................. 1
1.1 Literature review ....................................... 1
1.2 Objective of this thesis ................................ 4
1.3 Thesis outline .......................................... 5
2 Computational fluid dynamics ................................. 9
2.1 Governing equations ..................................... 9
2.2 Solution method ........................................ 12
3 Reduced-order modeling via POD - state of the art ........... 13
3.1 Proper orthogonal decomposition ....................... 13
3.2 Galerkin projection onto POD subspace .................. 16
3.3 Proper orthogonal decomposition with interpolation .... 17
3.4 Proper orthogonal decomposition with residual
optimization .......................................... 19
4 Reduced-order modeling via manifold learning ................ 21
4.1 Manifolds and geodesic distances ....................... 22
4.2 Manifold learning / dimensionality reduction .......... 26
4.3 Manifold learning by Isomap ............................ 28
4.3.1 Approximating geodesic distances ................ 29
4.3.2 Multidimensional scaling ........................ 30
4.3.3 Isomap and the choice of its parameters ......... 34
4.4 From reduced-order representation to full-dimensional
snapshot approximations ............................... 36
4.4.1 Non-parametric back-mapping ..................... 37
4.4.2 Solving the back-mapping weights optimization
problem ......................................... 39
4.4.3 Adaptive choice of the neighborhood size ........ 39
4.5 Isomap with interpolation .............................. 40
4.6 Isomap with CFD-enhanced back-mapping .................. 41
4.7 Additional possible applications of Isomap(+I) ......... 43
5 Adaptive sampling ........................................... 45
5.1 Manifold filling adaptive sampling strategy ............ 45
5.2 Proof of concept ....................................... 48
6 Computational issues ........................................ 55
6.1 Software integration .................................. 55
6.2 Complexity of Isomap+I ................................. 57
6.3 Notes on parallelization ............................... 58
7 Applications ................................................ 61
7.1 NACA 64A010 airfoil .................................... 62
7.1.1 Isomap with interpolation ....................... 64
7.1.2 Isomap with residual optimization ............... 69
7.1.3 Adaptive sampling ............................... 72
7.2 XRF-1 fuselage-wing configuration ...................... 76
7.2.1 Isomap with interpolation ....................... 83
7.2.2 Isomap with residual optimization ............... 92
7.3 Reduced-order models for aero-data for loads and
structural sizing ...................................... 93
8 Conclusions ................................................ 101
A Radial basis functions model ............................... 103
B Delaunay triangulation ..................................... 105
Bibliography .................................................. 114
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