Optimal control of vorticity in Rayleigh-Bernard convection by finite element method

✍ Scribed by Marin, Maxim ;Kawahara, Mutsuto

• Publisher: John Wiley and Sons
• Year: 1998
• Tongue: English
• Weight: 300 KB
• Volume: 14
• Category: Article
• ISSN: 1069-8299
• DOI: 10.1002/(sici)1099-0887(199801)14:1<9::aid-cnm124>3.0.co;2-i

✦ Synopsis

This work presents control of vorticity for buoyancy-driven ¯ows. The governing set of equations includes Navier±Stokes and heat transfer equations. The basic formulation for the control problem is derived using Lagrange multipliers and the Pontryagin minimum principle. Control values are found using the Sakawa± Shindo method. Control was accomplished using velocity components. Numerical examples present control of vorticity for Rayleigh±Bernard convection in an enclosed cavity for a wide range of Ra numbers. The current formulation proved reliable and fast. Optimal control was obtained and turned out to be adequate.