ABSTRACT
This chapter presents short introductions into the physical processes and to their model concepts together with references to analytical work. The simulation of crystal growth and solidification requires a set of different methods, each one with specific strengths and weaknesses on certain scales of length and time. The most characteristic feature of crystal growth and solidification with respect to modeling is the aspect of the moving-boundary problem. There is some analogy in the fluid dynamics of non-miscible two-fluid systems, but the solidification aspect additionally brings anisotropy into play. The macroscopic appearance of crystals, with their polygonal facets and the underlying lattice structure, is the consequence of quantum mechanical interactions between the atoms. The simplest atomistic model for the formation of a crystal in continuous space requires the definition of some effective attractive potential between any two atoms, which is defined independently of the other atoms in the cluster or crystal.
