Despite increasing applications of additively manufactured parts, they still suffer from anisotropic mechanical properties and can lead to cracking due to coarse columnar grain structures induced by metal 3D printing. Microstructural control is promising avenue to overcome these challenges, but requires deeper understanding of factors controlling solidification, particularly regarding grain refinement. Addressing this gap, this study explores grain refinement in Al-Cu alloys with a process-microstructure linking cellular automata-finite difference (CAFD) approach supported by single-track laser surface remelting (LSR) experiments. To enhance the understanding of nucleation behaviour in alloys under additive manufacturing solidification conditions, this research analyses the influence of nucleation parameters on the post-LSR microstructures. Additionally, this study explores the computational dimensions of microstructure modelling, testing CA mesh sensitivity effects and benchmarking our CAFD models on two high-performance computing platforms. The CAFD model captures well the key microstructural features observed in LSR Al-Cu alloys with and without grain refiner addition. It is shown that the maximum nucleation density has a significant effect on the final microstructure, resulting in different proportions of coarse columnar grains resulting from epitaxial solidification, newly nucleated thin columnar grains, and equiaxed grains.