[Amath-seminars] Feb. 11 - Special AMATH Seminar - Weiwei Hu (IMA)
hetmaniu at uw.edu
Mon Feb 8 10:37:16 PST 2016
We hope you can join us for our special AMATH seminar on **Thursday**
Speaker: Weiwei Hu, IMA
Time: February 11th, 16h00
Location: DEM 004
Title: Controlling a Thermal Fluid: Theoretical and Computational Issues
We first discuss the problem of designing a feedback law which locally
stabilizes a two dimensional thermal fluid modeled by the Boussinesq
equations. The investigation of stability for a fluid flow in the natural
convection problem is important in the theory of hydrodynamical stability.
The challenge of stabilization of the Boussinesq equations arises from the
stabilization of the Navier-Stokes equations and its coupling with the
convection-diffusion equation for temperature. In particular, given a
steady state solution on a bounded and connected domain, we show that a
finite number of controls acting on a part of the boundary through
Neumann/Robin boundary conditions is sufficient to stabilize the full
nonlinear equations in the neighborhood of this steady state solution.
Dirichlet boundary conditions are imposed on the rest of the boundary.
Moreover, we prove that a stabilizing feedback control law can be obtained
based on the state estimators by solving an extended Kalman filter
problem for the linearized Boussinesq equations. A reduced order model is
used to construct a finite dimensional estimator. Numerical results are
provided to illustrate the idea. In the end, we discuss the problem of
well-posedness and control designs for the Boussinesq equations with zero
diffusivity and its application to optimal mixing and stirring.
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