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The Electroslag Remelting (ESR) is an advanced technology for the production of high quality materials, for example, hot work tool steels or nickel base alloys. In the past years, several models are developed aiming to predict the way in which the operational parameters affect the structure and chemical composition of the final ESR ingot. Proper modeling of this process depends on the ability of the model to predict the Multiphysics resulting from the complex coupling between many physical phenomena. This review includes the main findings starting from the 1970's, with a special focus on the results obtained in the period of 1999–2017. The difficulties related to the poorly known physical properties of ESR slags are discussed. Then, the main achievements in the field of electromagnetism, fluid flow, heat transfer, and solidification are also summarized. The review finishes by presenting the special topics representing the actual scientific frontiers, such as the physics of mold current, the importance of multiphase phenomena, and the difficulties in predicting the electrode melting rate. [ABSTRACT FROM AUTHOR]

• A new model proposed for melting and grain destruction phenomena during globular equiaxed solidification. • Model-aided visualization of the remelting phenomenon during solidification process. • Solidification, grain migration and remelting: an important species/energy transport mechanism. Melting or re-melting accompanies solidification in many technical castings. For example, during ingot casting, some crystal fragments or equiaxed grains can enter the superheated region and re-melt, while solidification continues in other regions. Solidification and remelting occurring simultaneously at different locations present an important species/energy transport mechanism, which impacts the structural/compositional homogeneity of the castings. The re-melting is typically understood as a reduction in the equiaxed grain size, but it can also lead to the destruction (disappearance) of equiaxed grains. Existing process-based models cannot treat the solidification/melting by considering both grain nucleation and destruction properly. Therefore, a new model is proposed based on a two-phase volume-average approach. In this model, nucleation of equiaxed grains occurs when inoculants (free growth sites) are activated by undercooling, while destruction of equiaxed grains occurs only when the equiaxed grains are completely re-melted by superheating. The mass, momentum, species, and enthalpy conservation equations are solved for the solidification/melting. The transport equations for the number densities of equiaxed grains and inoculants are calculated separately. A test casting (Al–7 wt.% Si) is calculated to illustrate the modelling features. This study improves understanding of grain melting and grain destruction as well as their impact on the as-solidified structure. [ABSTRACT FROM AUTHOR]