Arbitrary Lagrangian-Eulerian approach in reduced order modeling of a flow with a moving boundary

Stankiewicz, Witold; Roszak, Robert; Morzyński, Marek

doi:10.1051/eucass/201305109

Cited by 3 publications

(1 citation statement)

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“…It is noteworthy that the reduced bases on the time-varying grid as presented in this article is different from what often appears in literature. 59,60 The motivation of this choice is out of the scope of this article and is discussed in Reference 45.…”

Section: F I G U R E 5 Solution Of 2 Nd -Order Wave Equationmentioning

confidence: 99%

Stabilization of linear time‐varying reduced‐order models: A feedback controller approach

Mojgani

Balajewicz

2020

Numerical Meth Engineering

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Summary Many of the commonly used methods in model‐order reduction do not guarantee stability of the reduced‐order model. This article extends the eigenvalue reassignment method of stabilization of linear time‐invariant ROMs, to the more general case of linear time‐varying systems. Through a postprocessing step, the ROM is controlled to ensure the stability while enhancing/maintaining its accuracy using a constrained nonlinear lease‐square minimization problem. The controller and the input signals are defined at the algebraic level, using left and right singular vectors of the reduced system matrices. The choice provides a control on the upper bound of the growth of the energy of the reduced system. The optimization problem is applied to several time‐invariant, time‐periodic, and time‐varying problems, and the reproductive and predictive capabilities of the proposed method, with respect to novel inputs and the system parameters, are evaluated.

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Section: F I G U R E 5 Solution Of 2 Nd -Order Wave Equationmentioning

confidence: 99%