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

The paper is devoted to the numerical analysis of new model of metals crystallization processes. The novelty of the model under consideration, which only recently appears in the literature, is in the situation when modeling is performed simultaneously for several scales, from micro to macro. Though now the experimental researches establish the multiplicity of the details of crystallization process, the general theoretical view of this process does not 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. The relevant numerical scheme is constructed and its convergence property is demonstrated. It is also shown the possibility to model different crystallization regimes when changing the parameters of the model. The multi-D variant with the usage of multiprocessor calculation complex is planed to be studied in the subsequent publications.