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.