Thomas P. Svobodny

Boundary velocity control of incompressible flow with an application to viscous drag reduction

An optimal boundary control problem for the Navier–Stokes equations is presented. The control is the velocity on the boundary, which is constrained to lie in a closed, convex subset of

The approximation of boundary control problems for fluid flows with an application to control by heating and cooling

H^{{1 / 2}}

Finite element approximations of an optimal control problem associated with the scalar Ginzburg-Landau equation

of the boundary. A necessary condition for optimality is derived. Computations are done when the control set is actually finite-dimensional, resulting in an application to viscous drag reduction.

Numerical aproximation of an optimal control problem associated with the Navier-Stokes equations

Abstract The goal of a boundary control or optimization problem for a fluid flow is to achieve some desired objective by the application of a control mechanism along a portion of the boundary of the flow domain. Among the objectives of interest are some related to drag reduction, some to the avoidance of high temperatures along boundary surfaces and some to conformation to a desired flow pattern. Possible control mechanisms are injected or suction of fluid through boundary orifices and heating or cooling along boundary surfaces. The objective is met through the minimization of an associated cost functional. The method of Lagrange multipliers is used to derive a system of partial differential equations whose solutions provide the optimal states and controls. No simplifications concerning the flow are invoked, i.e. the full Navier-Stokes equations are employed. Finite element algorithms for approximating the optimal states and controls are discussed, as is the accuracy of approximations resulting from these algorithms. Details are provided for the example of using heating and cooling controls in order to avoid hot spots along bounding surfaces.

Evolution of mixed-state regions in type-II superconductors

Abstract We consider finite element approximations of an optimal control problem associated with a scalar version of the Ginzburg-Landau equations of superconductivity. The control is the Neumann data on the boundary and the optimization goal is to obtain a best approximation, in the least squares sense, to some desired state. The existence of optimal solutions is proved. The use of Lagrange multipliers is justified and an optimality system of equations is derived. Then, the regularity of solutions of the optimality system is studied, and finally, finite element algorithms are defined and optimal error estimates are obtained.

Stability of growing front of YBa2Cu3Ox superconductor in the presence of Pt and CeO2 additions

Control problems distinguish themselves in the following way from the usual problems that workers in PDEs deal with (e.g. questions of regularity) . A gross property is postulated for the solution of the relevant PDE or system of PDEs and one chooses parameters that appear in the equations in order to adhere to this property. In the problem at hand we consider the encouragement, in the least squares sense, of a viscous incompressible flow towards a given vector field by appropriately choosing the stress tensor on the boundary of the (bounded) d om_ain. We wish to minimize the functional

Shape Optimization and Control of Separating Flow in Hydrodynamics

A mean-field model for dynamics of superconducting vortices is studied. The model, consisting of an elliptic equation coupled with a hyperbolic equation with discontinuous initial data, is formulated as a system of nonlocal integrodifferential equations. We show that there exists a unique classical solution in

Pulsed-laser ablation plume dynamics: characterization and modeling

C^{1+\alpha }\left( \bar{\Omega}_0\right)

Free boundary problems for potential and Stokes flows via nonsmooth analysis

for all

Optimal boundary control of nonsteady incompressible flow with an application to viscous drag reduction

t>0,