Control of fluids
Below some applications of optimal and suboptimal
control methods to fluid flow are presented. The flow always is governed by the instationary
Navier-Stokes equations, the control is acts on the system in terms
of distributed forces(volume control) or boundary data(boundary control).
The control methods include optimal open loop control, receding horizon-type
control (instantaneous control) and control via model reduction. Examples
with bounded controls are also included. The latter are computed with primal-dual active set strategies.
Gif-animations of optimal control of fluids
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Animation
Optimal
control of the flow around a cylinder: Distributed control in the whole
domain (1.4 Mb)
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Animation
Optimal
control of the flow around a cylinder: Distributed control in a oart of
the domain (1.1 Mb)
Movies with optimal control
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Movie
Optimal
control of the flow around a cylinder: Distributed control in the whole
domain (1.4 Mb)
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Movie
Optimal
control of the flow around a cylinder: Distributed control in a part of
the domain (1.1 Mb)
Movies with instantaneous control
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Movie
Instantaneous
control the flow around a cylinder: Distributed control in a part of the
domain (0.45 Mb)
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Movie
Instantaneous
boundary control of a BFS-flow using boundary information: Large observation
area (5.1 Mb)
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Movie
Instantaneous
boundary control of a BFS-flow using boundary information: Medium observation
area (9.6 Mb)
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Movie
Instantaneous
boundary control of a BFS-flow using boundary information: Small observation
area (12.9 Mb)
Movies with reduced order modelling control (joint with
Andreas Kauffmann)
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Movie
Reduced
order modeled Navier-Stokes equations compared to full equations for flow
around a cylinder. Reduction with Proper Orthogonal Decomposition (1.04Mb)
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Movie
Control
computed with reduced order modeled Navier-Stokes equations applied to
control of the full flow around a cylinder. Reduction with Proper Orthogonal
Decomposition (0.75Mb)
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Movie
Flow
and control computed with reduced order modeled Navier-Stokes equations
for flow around a cylinder. Reduction with Proper Orthogonal Decomposition
(0.86Mb)
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Movie
Comparison
of flow and reduced flow controlled with POD suboptimal controls. Reduction
with Proper Orthogonal Decomposition (0.58Mb)
Movies with bounded controls (joint with Michael
Hintermüller, Graz)
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Movie
showing distributed control with control constraints for the cavity flow.
Control target is Stokes flow. Result for bounded controls is compared
to that for free controls. A movie illustrating the evolution of the active
sets can be downloaded
here
. The controls u have to satisfy -0.3 <= u <= 0.3.
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Movie
showing the same as above, but the controls have to satisfy -0.03 <=
u1 <= 0.03, -0.3 <= u2 <= 0.3. The related evolution of the
active sets can be downloaded here
.
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Movie
for -0.03 <= u <= 0.03, evolution of the active sets as mpeg
.
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More Movies (23Mb).
Related publications see item Publications
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