This paper presents a numerical procedure for achieving desired features of a melt undergoing solidification by applying an external magnetic field whose intensity and spatial distribution are obtained by the use of a hybrid optimization algorithm. The intensities of the magnets along the boundaries of the container are described as B-splines. The inverse problem is then formulated as to find the magnetic boundary conditions (the coefficients of the B-splines) in such a way that the gradients of temperature along the gravity direction are minimized. For this task, a hybrid optimization code was used that incorporates several of the most popular optimization modules; the Davidon-Fletcher-Powell (DFP) gradient method, a genetic algorithm (GA), the Nelder-Mead (NM) simplex method, quasi-Newton algorithm of Pshenichny-Danilin (LM), differential evolution (DE), and sequential quadratic programming (SQP). Transient Navier-Stokes and Maxwell equations were discretized using finite volume method in a generalized curvilinear non-orthogonal coordinate system. For the phase change problems, an enthalpy formulation was used. The code was validated against analytical and numerical benchmark results with very good agreements in both cases.

This content is only available via PDF.
You do not currently have access to this content.