# Pseudo-spectral solutions for fluid flow and heat transfer in electro-metallurgical applications

Pericleous, Koulis A. and Bojarevics, Valdis (2007) *Pseudo-spectral solutions for fluid flow and heat transfer in electro-metallurgical applications.* Progress in Compultational Fluid Dynamics, 7 (2-4). pp. 118-127. ISSN 1468-4349 (doi:10.1504/PCFD.2007.013004)

## Abstract

The pseudo-spectral solution method offers a flexible and fast alternative to the more usual finite element and volume methods, particularly when the long-time transient behaviour of a system is of interest. The exact solution is obtained at grid collocation points leading to superior accuracy on modest grids. Furthermore, the grid can be freely adapted in time and space to particular flow conditions or geometric variations, especially useful where strongly coupled, time-dependent, multi-physics solutions are investigated. Examples include metallurgical applications involving the interaction of electromagnetic fields and conducting liquids with a free surface. The electromagnetic field determines the instantaneous liquid volume shape, which then affects the electromagnetic field. A general methodology of the pseudo-spectral approach is presented, with several instructive example applications: the aluminium electrolysis MHD problem, induction melting in a cold crucible and the dynamics of AC/DC magnetically levitated droplets. Finally, comparisons with available analytical solutions and to experimental measurements are discussed.

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