Computations of Boundary Optimal Control Problems for an Electrically Conducting Fluid

✍ Scribed by L.S. Hou; S.S. Ravindran

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 443 KB
• Volume: 128
• Category: Article
• ISSN: 0021-9991
• DOI: 10.1006/jcph.1996.0213

✦ Synopsis

The methods proposed in this paper are applicable to more general optimal control problems in viscous incom-

We study four optimal control problems for an electrically conducting fluid. The control is the (normal) electrical current on the pressible flows with various types of controls than the parboundary of the flow domain. The objectives are to match a desired ticular problems studied in this paper. velocity field, or to match a desired electrical potential field, or to Optimal control and optimization for MHD flows have minimize the potential gradient, or to minimize the vorticity in the been the subject of extensive research in the literature. flow domain. We develop a systematic way to use the Lagrange

Most notably there are well-established bodies of literature multiplier rules to derive an optimality system of equations from which an optimal solution can be computed. Mixed finite element on optimization of liquid-metal MHD in the following methods are used to find approximate solutions for the optimality areas: the optimal choice of positions and electric currents systems of equations that characterize the optimal controls. A direct for AC induction coils in order to achieve a desired freemethod and an iterative method are proposed for solving the dissurface shape in electromagnetic levitation of liquid-metal crete, nonlinear optimality systems of equations. Numerical results droplets; the optimal positioning of AC coils and magnetic

for several examples are presented.