Solidification of double-diffusive flows using thermo-magneto-hydrodynamics and optimization

A multilevel approach, based on our previously developed hybrid optimizer, is presented for solving a problem that consists of a solidifying thermosolutal flow in a square cavity subjected to variable thermal and magnetic boundary conditions. The objective is to reduce the standard deviations of the vorticity within the liquid region as well as reduce the liquid area over the entire domain. Thus, the optimization problem is formulated to simultaneously find thermal and magnetic boundary conditions that must induce such prescribed solute concentration and velocity profiles. The optimizer is based on several deterministic and evolutionary techniques with automatic switching among them, combining the best feature of each algorithm. A radial basis function based response surface scheme is implemented to reduce the overall computing time.