NUMERICAL SOLUTIONS OF OPTIMAL CONTROL FOR THERMALLY CONVECTIVE FLOWS

✍ Scribed by S. S. Ravindran

• Publisher: John Wiley and Sons
• Year: 1997
• Tongue: English
• Weight: 420 KB
• Volume: 25
• Category: Article
• ISSN: 0271-2091
• DOI: 10.1002/(sici)1097-0363(19970730)25:2<205::aid-fld547>3.0.co;2-n

✦ Synopsis

We study the numerical solution of optimal control problems associated with two-dimensional viscous incompressible thermally convective ¯ows. Although the techniques apply to more general settings, the presentation is con®ned to the objectives of minimizing the vorticity in the steady state case and tracking the velocity ®eld 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; ®nite element methods are used to ®nd 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 de®ned. Numerical results are presented for both the steady state and time-dependent optimal control problems.