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On linear and nonlinear aspects of dynamic mode decomposition
Author(s) -
Alekseev A. K.,
Bistrian D. A.,
Bondarev A. E.,
Navon I. M.
Publication year - 2016
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.4221
Subject(s) - nonlinear system , propagator , dynamic mode decomposition , interpolation (computer graphics) , linear interpolation , mode (computer interface) , mathematics , supersonic speed , mathematical analysis , operator (biology) , physics , classical mechanics , mechanics , computer science , motion (physics) , biochemistry , chemistry , quantum mechanics , repressor , polynomial , transcription factor , mathematical physics , gene , operating system
Summary The approximation of reduced linear evolution operator (propagator) via dynamic mode decomposition (DMD) is addressed for both linear and nonlinear events. The 2D unsteady supersonic underexpanded jet, impinging the flat plate in nonlinear oscillating mode, is used as the first test problem for both modes. Large memory savings for the propagator approximation are demonstrated. Corresponding prospects for the estimation of receptivity and singular vectors are discussed. The shallow water equations are used as the second large‐scale test problem. Excellent results are obtained for the proposed optimized DMD method of the shallow water equations when compared with recent POD‐based/discrete empirical interpolation‐based model reduction results in the literature. Copyright © 2016 John Wiley & Sons, Ltd.