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An Optimal Control Approach to Bounding Transport Properties of Thermal Convection.

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	An Optimal Control Approach to Bounding Transport Properties of Thermal Convection./
Author:	Souza, Andre N.
Description:	1 online resource (145 pages)
Notes:	Source: Dissertation Abstracts International, Volume: 78-07(E), Section: B.
Contained By:	Dissertation Abstracts International78-07B(E).
Subject:	Applied mathematics. -
Online resource:	click for full text (PQDT)
ISBN:	9781369590036

An Optimal Control Approach to Bounding Transport Properties of Thermal Convection.
Souza, Andre N.

An Optimal Control Approach to Bounding Transport Properties of Thermal Convection. - 1 online resource (145 pages)

Source: Dissertation Abstracts International, Volume: 78-07(E), Section: B.

Thesis (Ph.D.)

Includes bibliographical references

This dissertation explores and develops an optimal control approach to upper bounds on transport properties of fluid flows inspired by the physical phenomenon of buoyancy-driven Rayleigh-Benard convection. This method is applied in the context of three different problems: the Lorenz equations, the Double Lorenz equations, and the Boussinesq approximation to the Navier-Stokes equations. Rather than restricting attention to flows that satisfy an equation of motion, we consider incompressible flows that satisfy suitable bulk integral constraints and boundary conditions. Bounds on transport are formulated in terms of optimal control problems where the flows are the "control" and a passive scalar tracer field is the "state". All three problems lead to non-convex optimization problems. Sharp upper bounds to the Lorenz equations are proven analytically, and it is shown that any sustained time-dependence of the control variable strictly lowers transport. For the Double Lorenz equations an upper bound is proven and saturated by steady optimizing flow fields and any time-periodic stirring protocol strictly lowers transport. In contrast to the Lorenz equations, however, the optimizing steady flow fields (solutions to the Euler-Lagrange equations for optimal transport) are not solutions to the original equations of motion. In the Boussinesq equation context the optimal control problem is rigorously formulated for steady flows, and analytic upper bounds to transport are deduced using the background method. A gradient ascent procedure for numerically solving the associated the Euler-Lagrange equations for optimal transport is developed, including optimality conditions for the domain size. The numerically computed optimizing flow fields consist of convection cells of decreasing aspect ratio as one allows for a stronger flow fields. Implications for natural convective transport in the motivating Rayleigh-Benard problem are discussed.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2018

Mode of access: World Wide Web

ISBN: 9781369590036Subjects--Topical Terms:

1069907
Applied mathematics.
Index Terms--Genre/Form:

554714
Electronic books.

An Optimal Control Approach to Bounding Transport Properties of Thermal Convection.
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245 1 3 $a An Optimal Control Approach to Bounding Transport Properties of Thermal Convection.
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300 $a 1 online resource (145 pages)
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500 $a Source: Dissertation Abstracts International, Volume: 78-07(E), Section: B.
500 $a Advisers: Divakar Viswanath; Charles R Doering.
502 $a Thesis (Ph.D.) $c University of Michigan $d 2016.
504 $a Includes bibliographical references
520 $a This dissertation explores and develops an optimal control approach to upper bounds on transport properties of fluid flows inspired by the physical phenomenon of buoyancy-driven Rayleigh-Benard convection. This method is applied in the context of three different problems: the Lorenz equations, the Double Lorenz equations, and the Boussinesq approximation to the Navier-Stokes equations. Rather than restricting attention to flows that satisfy an equation of motion, we consider incompressible flows that satisfy suitable bulk integral constraints and boundary conditions. Bounds on transport are formulated in terms of optimal control problems where the flows are the "control" and a passive scalar tracer field is the "state". All three problems lead to non-convex optimization problems. Sharp upper bounds to the Lorenz equations are proven analytically, and it is shown that any sustained time-dependence of the control variable strictly lowers transport. For the Double Lorenz equations an upper bound is proven and saturated by steady optimizing flow fields and any time-periodic stirring protocol strictly lowers transport. In contrast to the Lorenz equations, however, the optimizing steady flow fields (solutions to the Euler-Lagrange equations for optimal transport) are not solutions to the original equations of motion. In the Boussinesq equation context the optimal control problem is rigorously formulated for steady flows, and analytic upper bounds to transport are deduced using the background method. A gradient ascent procedure for numerically solving the associated the Euler-Lagrange equations for optimal transport is developed, including optimality conditions for the domain size. The numerically computed optimizing flow fields consist of convection cells of decreasing aspect ratio as one allows for a stronger flow fields. Implications for natural convective transport in the motivating Rayleigh-Benard problem are discussed.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2018
538 $a Mode of access: World Wide Web
650 4 $a Applied mathematics. $3 1069907
655 7 $a Electronic books. $2 local $3 554714
690 $a 0364
710 2 $a ProQuest Information and Learning Co. $3 1178819
710 2 $a University of Michigan. $b Applied and Interdisciplinary Mathematics. $3 1180800
773 0 $t Dissertation Abstracts International $g 78-07B(E).
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10391793 $z click for full text (PQDT)