Smooth and robust solutions for Dirichlet boundary control of fluid-solid conjugate heat transfer problems

Handle URI:
http://hdl.handle.net/10754/563979
Title:
Smooth and robust solutions for Dirichlet boundary control of fluid-solid conjugate heat transfer problems
Authors:
Yan, Yan; Keyes, David E. ( 0000-0002-4052-7224 )
Abstract:
We study a new optimization scheme that generates smooth and robust solutions for Dirichlet velocity boundary control (DVBC) of conjugate heat transfer (CHT) processes. The solutions to the DVBC of the incompressible Navier-Stokes equations are typically nonsmooth, due to the regularity degradation of the boundary stress in the adjoint Navier-Stokes equations. This nonsmoothness is inherited by the solutions to the DVBC of CHT processes, since the CHT process couples the Navier-Stokes equations of fluid motion with the convection-diffusion equations of fluid-solid thermal interaction. Our objective in the CHT boundary control problem is to select optimally the fluid inflow profile that minimizes an objective function that involves the sum of the mismatch between the temperature distribution in the fluid system and a prescribed temperature profile and the cost of the control.Our strategy to resolve the nonsmoothness of the boundary control solution is based on two features, namely, the objective function with a regularization term on the gradient of the control profile on both the continuous and the discrete levels, and the optimization scheme with either explicit or implicit smoothing effects, such as the smoothed Steepest Descent and the Limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) methods. Our strategy to achieve the robustness of the solution process is based on combining the smoothed optimization scheme with the numerical continuation technique on the regularization parameters in the objective function. In the section of numerical studies, we present two suites of experiments. In the first one, we demonstrate the feasibility and effectiveness of our numerical schemes in recovering the boundary control profile of the standard case of a Poiseuille flow. In the second one, we illustrate the robustness of our optimization schemes via solving more challenging DVBC problems for both the channel flow and the flow past a square cylinder, which use initial control profiles far from optimal and require the numerical continuation technique applied on regularization parameters. We believe our solution strategy is general and can be applied to other large-scale optimal control problems which involve multiphysics processes and require smooth approximations to the optimal control profile.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Applied Mathematics and Computational Science Program; Extreme Computing Research Center
Publisher:
Elsevier BV
Journal:
Journal of Computational Physics
Issue Date:
Jan-2015
DOI:
10.1016/j.jcp.2014.10.049
Type:
Article
ISSN:
00219991
Sponsors:
The authors gratefully acknowledge awards DE-FG07-07ID14889 and DE-FC02-06ER25783 from the U.S. Department of Energy (DOE) for part of the research, access to computing resources at the New York Center for Computational Sciences at Stony Brook University/Brookhaven National Laboratory supported by the U.S. DOE under Contract DE-AC02-98CH10886 and by the State of New York, and access to resources of the National Energy Research Scientific Computing Center supported by the Office of Science of the U.S. DOE under Contract DE-AC02-05CH11231.
Appears in Collections:
Articles; Applied Mathematics and Computational Science Program; Extreme Computing Research Center; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorYan, Yanen
dc.contributor.authorKeyes, David E.en
dc.date.accessioned2015-08-03T12:21:41Zen
dc.date.available2015-08-03T12:21:41Zen
dc.date.issued2015-01en
dc.identifier.issn00219991en
dc.identifier.doi10.1016/j.jcp.2014.10.049en
dc.identifier.urihttp://hdl.handle.net/10754/563979en
dc.description.abstractWe study a new optimization scheme that generates smooth and robust solutions for Dirichlet velocity boundary control (DVBC) of conjugate heat transfer (CHT) processes. The solutions to the DVBC of the incompressible Navier-Stokes equations are typically nonsmooth, due to the regularity degradation of the boundary stress in the adjoint Navier-Stokes equations. This nonsmoothness is inherited by the solutions to the DVBC of CHT processes, since the CHT process couples the Navier-Stokes equations of fluid motion with the convection-diffusion equations of fluid-solid thermal interaction. Our objective in the CHT boundary control problem is to select optimally the fluid inflow profile that minimizes an objective function that involves the sum of the mismatch between the temperature distribution in the fluid system and a prescribed temperature profile and the cost of the control.Our strategy to resolve the nonsmoothness of the boundary control solution is based on two features, namely, the objective function with a regularization term on the gradient of the control profile on both the continuous and the discrete levels, and the optimization scheme with either explicit or implicit smoothing effects, such as the smoothed Steepest Descent and the Limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) methods. Our strategy to achieve the robustness of the solution process is based on combining the smoothed optimization scheme with the numerical continuation technique on the regularization parameters in the objective function. In the section of numerical studies, we present two suites of experiments. In the first one, we demonstrate the feasibility and effectiveness of our numerical schemes in recovering the boundary control profile of the standard case of a Poiseuille flow. In the second one, we illustrate the robustness of our optimization schemes via solving more challenging DVBC problems for both the channel flow and the flow past a square cylinder, which use initial control profiles far from optimal and require the numerical continuation technique applied on regularization parameters. We believe our solution strategy is general and can be applied to other large-scale optimal control problems which involve multiphysics processes and require smooth approximations to the optimal control profile.en
dc.description.sponsorshipThe authors gratefully acknowledge awards DE-FG07-07ID14889 and DE-FC02-06ER25783 from the U.S. Department of Energy (DOE) for part of the research, access to computing resources at the New York Center for Computational Sciences at Stony Brook University/Brookhaven National Laboratory supported by the U.S. DOE under Contract DE-AC02-98CH10886 and by the State of New York, and access to resources of the National Energy Research Scientific Computing Center supported by the Office of Science of the U.S. DOE under Contract DE-AC02-05CH11231.en
dc.publisherElsevier BVen
dc.subjectConjugate heat transferen
dc.subjectMultiphysicsen
dc.subjectNavier-Stokesen
dc.subjectNumerical continuationen
dc.subjectNumerical smoothingen
dc.subjectOptimal controlen
dc.subjectRegularizationen
dc.titleSmooth and robust solutions for Dirichlet boundary control of fluid-solid conjugate heat transfer problemsen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.contributor.departmentApplied Mathematics and Computational Science Programen
dc.contributor.departmentExtreme Computing Research Centeren
dc.identifier.journalJournal of Computational Physicsen
dc.contributor.institutionDepartment of Applied Physics and Applied Mathematics, Columbia University, 500 W. 120th Street, Mudd 200New York, NY, United Statesen
kaust.authorKeyes, David E.en
All Items in KAUST are protected by copyright, with all rights reserved, unless otherwise indicated.