Numerical analysis of new model of metals cristallization processes, two-dimensional case

The paper is devoted to the numerical simulation of new model of metals crystallization processes. The difficulties of such simulation arise from the multiscale phenomenology of crystallization process. Nowadays the experimental researches establish the multiplicity of the details of crystallization process, however the general theoretical view of this process does not yet exist. The model which is used in the present paper is based on the description of a space occupied by the crystallizing alloy as the porous medium. The propagation of perturbations in such a medium is described by the equations of Biot’s type. The emergence of germs is described by modified Kahn-Hilliard equation. Previously the 1D numerical scheme has been constructed and its convergence property has been demonstrated. It is shown the possibility to model different crystallization regimes when changing the parameters of the model. In the presented paper 2D numerical model and results of computations are given. Due to multiscale phenomena the calculations require significant CPU time and hence the 2D model is based on explicit and explicit iteration algorithms which are implemented efficiently on multiprocessor computers.