A Multigrid Approach to Optimal Control Computations for Navier-Stokes Flows

2006 ◽  
pp. 3-23
Author(s):  
E. Aulisa ◽  
S. Manservisi
Keyword(s):  
Optimal Control ◽  
Navier Stokes ◽  
Stokes Flows

Optimal Control of Two- and Three-Dimensional Incompressible Navier–Stokes Flows

1997 ◽  
Vol 136 (2) ◽  
pp. 231-244 ◽  
Author(s):  
Omar Ghattas ◽  
Jai-Hyeong Bark
Keyword(s):  
Optimal Control ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Stokes Flows

Optimal control of vortices in non-homogeneous Navier–Stokes flows

2007 ◽  
Vol 66 (11) ◽  
pp. 2618-2634
Author(s):  
S. Chaabane ◽  
J. Ferchichi ◽  
K. Kunisch
Keyword(s):  
Optimal Control ◽  
Navier Stokes ◽  
Stokes Flows

scholarly journals Velocity–pressure correlation in Navier–Stokes flows and the problem of global regularity

2021 ◽  
Vol 911 ◽  
Author(s):  
Chuong V. Tran ◽  
Xinwei Yu ◽  
David G. Dritschel
Keyword(s):  
Global Regularity ◽  
Navier Stokes ◽  
Stokes Flows ◽  
Velocity Pressure

Abstract

scholarly journals Asymptotic analysis of an optimal control problem for a viscous incompressible fluid with Navier slip boundary conditions

2021 ◽  
pp. 1-21
Author(s):  
Claudia Gariboldi ◽  
Takéo Takahashi
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Boundary Conditions ◽  
Control Problem ◽  
Stokes System ◽  
Navier Stokes ◽  
Slip Boundary Conditions ◽  
Navier Slip ◽  
Slip Boundary ◽  
Navier Slip Boundary Conditions

We consider an optimal control problem for the Navier–Stokes system with Navier slip boundary conditions. We denote by α the friction coefficient and we analyze the asymptotic behavior of such a problem as α → ∞. More precisely, we prove that if we take an optimal control for each α, then there exists a sequence of optimal controls converging to an optimal control of the same optimal control problem for the Navier–Stokes system with the Dirichlet boundary condition. We also show the convergence of the corresponding direct and adjoint states.

Pontryagin maximum principle and second order optimality conditions for optimal control problems governed by 2D nonlocal Cahn–Hilliard–Navier–Stokes equations

Analysis ◽  
2020 ◽  
Vol 40 (3) ◽  
pp. 127-150
Author(s):  
Tania Biswas ◽  
Sheetal Dharmatti ◽  
Manil T. Mohan
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Stokes Equations ◽  
Minimum Principle ◽  
Immiscible Fluids ◽  
Second Order ◽  
Navier Stokes ◽  
Distributed Optimal Control ◽  
Navier Stokes Equations

AbstractIn this paper, we formulate a distributed optimal control problem related to the evolution of two isothermal, incompressible, immiscible fluids in a two-dimensional bounded domain. The distributed optimal control problem is framed as the minimization of a suitable cost functional subject to the controlled nonlocal Cahn–Hilliard–Navier–Stokes equations. We describe the first order necessary conditions of optimality via the Pontryagin minimum principle and prove second order necessary and sufficient conditions of optimality for the problem.

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