Instantaneous Closed Loop Control of the Navier--Stokes System

Instantaneous Closed Loop Control of the Navier-Stokes System

Instantaneous control is applied to the control of the instationary Navier-Stokes system. This control technique is closely related to receding horizon control and allows for an interpretation as suboptimal closed loop controller, whose parameters may be adjusted so as to stabilize the nonlinear equation under consideration. Besides stability analysis for the distributed control case numerical ...

Optimal and instantaneous control of the instationary Navier-Stokes equations

Contents Danksagung 1 Chapter 1. Introduction 5 1. Aims and scope of flow control 5 2. A brief review in active flow control 8 Chapter 2. Notation and preliminary results 15 1. Quasi-Stokes problems 15 2. Instationary Navier-Stokes equations in 2d 16 3. Navier-Stokes numerics 19 Chapter 3. Optimal control of the instationary Navier-Stokes equations 23 1. The optimal control problem 23 2. Deriva...

Adjoint gradients compared to gradients from algorithmic differentiation in instantaneous control of the Navier-Stokes equations

Optimal Control of a Semidiscrete Cahn-Hilliard-Navier-Stokes System

In this paper, the optimal boundary control of a time-discrete Cahn-Hilliard NavierStokes system is studied. A general class of free energy potentials is considered which, in particular, includes the double-obstacle potential. The latter homogeneous free energy density yields an optimal control problem for a family of coupled systems, which result from a time discretization of a variational ine...

Optimization with the time-dependent Navier-Stokes equations as constraints

In this paper, optimal distributed control of the time-dependent Navier-Stokes equations is considered. The control problem involves the minimization of a measure of the distance between the velocity field and a given target velocity field. A mixed numerical method involving a quasi-Newton algorithm, a novel calculation of the gradients and an inhomogeneous Navier-Stokes solver, to find the opt...