A stabilization algorithm of the Navier-Stokes equations based on algebraic Bernoulli equation

作者：Amodei L^*; Buchot J M

来源：Numerical Linear Algebra with Applications, 2012, 19(4): 700-727.

DOI：10.1002/nla.799

• Riccati equation
• Bernoulli equation
• Lyapunov equation
• feedback stabilization
• Navier-Stokes equations

In this paper, we consider the stabilization of the nonstationary incompressible NavierStokes equations around a stationary solution by a boundary linear feedback control. The feedback operator is obtained from the solution of the algebraic Bernoulli equation associated with the penalized linearized NavierStokes equations around an unstable stationary solution and is used to locally stabilize the original nonlinear equations. We give the explicit factorized form of the stabilizing solution of the algebraic Bernoulli equation. The numerical effectiveness of this approach is demonstrated by stabilizing the vortex shedding behind a circular obstacle.

• 出版日期2012-8