Premium
NUMERICAL SOLUTIONS OF OPTIMAL CONTROL FOR THERMALLY CONVECTIVE FLOWS
Author(s) -
Ravindran S. S.
Publication year - 1997
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/(sici)1097-0363(19970730)25:2<205::aid-fld547>3.0.co;2-n
Subject(s) - optimal control , lagrange multiplier , mathematics , piecewise , finite element method , numerical analysis , boundary value problem , mathematical optimization , control theory (sociology) , mathematical analysis , computer science , control (management) , physics , artificial intelligence , thermodynamics
We study the numerical solution of optimal control problems associated with two‐dimensional viscous incompressible thermally convective flows. Although the techniques apply to more general settings, the presentation is confined to the objectives of minimizing the vorticity in the steady state case and tracking the velocity field in the non‐stationary case with boundary temperature controls. In the steady state case we develop a systematic way to use the Lagrange multiplier rules to derive an optimality system of equations from which an optimal solution can be computed; finite element methods are used to find approximate solutions for the optimality system of equations. In the time‐dependent case a piecewise‐in‐time optimal control approach is proposed and the fully discrete approximation algorithm for solving the piecewise optimal control problem is defined. Numerical results are presented for both the steady state and time‐dependent optimal control problems. © 1997 John Wiley & Sons, Ltd.