2009
DOI: 10.1007/978-90-481-3723-7_74
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Abstract: International audienceThe application of control tools to fluid problems often requires model reduction to correctly capture the input-output behavior of the associated initial-value problem In this study a model combining global modes (for the unstable subspace) and balanced modes (for the stable subspace) is considered. We show that this model succeeds in removing the global instability or the flow over an incompressible cavity. Comparison with other reduced models clearly demonstrates the superiority of thi… Show more

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Cited by 1 publication
(2 citation statements)
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“…The above expression can, in turn, be written as Eu n =Āu n +Bc n + F (u n ) (4) where F : R n → R n represents the nonlinear term. The stiffness matrix Ā ∈ M n×n , the control matrix B ∈ M n×m c , as well as the mass matrix E ∈ M n×n , are assembled as usual, by computing the element integrals with Gauss-Legendre formulas.…”
Section: Problem and Semi-discretizationmentioning
confidence: 99%
See 1 more Smart Citation
“…The above expression can, in turn, be written as Eu n =Āu n +Bc n + F (u n ) (4) where F : R n → R n represents the nonlinear term. The stiffness matrix Ā ∈ M n×n , the control matrix B ∈ M n×m c , as well as the mass matrix E ∈ M n×n , are assembled as usual, by computing the element integrals with Gauss-Legendre formulas.…”
Section: Problem and Semi-discretizationmentioning
confidence: 99%
“…The control and stabilization of solutions for models described by partial differential equations has been widely studied for both the linear and the nonlinear case (see [3,9,12,25]). In the particular field of fluid dynamics the stabilization by means of boundary control has been subject of research both from the theoretical [28][29][30] and numerical point of view [1,4,7] while having airflow applications in mind. The case in which only partial measurements are available, remains however associated to many open questions.…”
Section: Introductionmentioning
confidence: 99%