An improved algorithm for the shallow water equations model reduction: Dynamic Mode Decomposition vs POD
نویسندگان
چکیده
We propose an improved framework for dynamic mode decomposition (DMD) of 2-D flows for problems originating from meteorology when a large time step acts like a filter in obtaining the significant Koopman modes, therefore, the classic DMD method is not effective. This study is motivated by the need to further clarify the connection between Koopman modes and proper orthogonal decomposition (POD) dynamic modes. We apply DMD and POD to derive reduced order models (ROM) of the shallow water equations. Key innovations for the DMD-based ROM introduced in this paper are the use of the Moore–Penrose pseudoinverse in the DMD computation that produced an accurate result and a novel selection method for the DMD modes and associated amplitudes and Ritz values. A quantitative comparison of the spatial modes computed from the two decompositions is performed, and a rigorous error analysis for the ROM models obtained is presented. Copyright © 2015 John Wiley & Sons, Ltd.
منابع مشابه
Comparison of optimized Dynamic Mode Decomposition vs POD for the shallow water equations model reduction with large-time-step observations
We propose a framework for dynamic mode decomposition of 2D flows, when numerical or experimental data snapshots are captured with large time steps. Such problems originate for instance from meteorology, when a large time step acts like a filter in obtaining the significant Koopman modes, therefore the classic dynamic mode decomposition method is not effective. This study is motivated by the ne...
متن کاملOn linear and nonlinear aspects of dynamic mode decomposition
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 pro...
متن کاملPOD/DEIM Nonlinear model order reduction of an ADI implicit shallow water equations model
In the present paper we consider a 2-D shallow-water equations (SWE) model on a βplane solved using an alternating direction fully implicit (ADI) finite-difference scheme (Gustafsson 1971, Fairweather and Navon 1980, Navon and De Villiers 1986, Kreiss and Widlund 1966) on a rectangular domain. The scheme was shown to be unconditionally stable for the linearized equations. The discretization yie...
متن کاملComparison of POD reduced order strategies for the nonlinear 2D Shallow Water Equations
This paper introduces tensorial calculus techniques in the framework of Proper Orthogonal Decomposition (POD) to reduce the computational complexity of the reduced nonlinear terms. The resulting method, named tensorial POD, can be applied to polynomial nonlinearities of any degree p. Such nonlinear terms have an on-line complexity of O(k), where k is the dimension of POD basis, and therefore is...
متن کاملExtension Ability of Reduced Order Model of Unsteady Incompressible Flows Using a Combination of POD and Fourier Modes
In this article, an improved reduced order modelling approach, based on the proper orthogonal decomposition (POD) method, is presented. After projecting the governing equations of flow dynamics along the POD modes, a dynamical system was obtained. Normally, the classical reduced order models do not predict accurate time variations of flow variables due to some reasons. The response of the dynam...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2015