Perspectives for cellular automata for the simulation of dendritic solidification – A review

• We offer a systematic literature review of CA models for dendritic solidification.
• Basic components are defined and assessed with respect to grid anisotropy.
• Diffusion and the cellwise mass balance is satisfactorily solved in literature.
• Algorithms for interface geometry calculation bear a potential for improvement.
• The cell state evolution algorithms have the highest potential for future research.

Numerous models for the simulation of dendritic solidification with Cellular Automaton based methods have been published in the last two decades. A large variety of different concepts have been investigated, an important fraction of them with the intent to reduce the anisotropic influence of the frequently employed Cartesian grid.The present review offers a systematization of the published models by identifying the basic components of a Cellular Automaton model describing dendritic solidification of alloys. These components are found to be three evolution algorithms, that is, one for each of the three central cell state variables, and an algorithm for the calculation of the interface geometry. The different approaches to these four algorithms are presented and evaluated with special regard toward possible potential for future research.Two of these algorithms are found to be of special interest for further model development: (1) both of the most commonly adopted geometry calculation methods, cell counting and level set with Finite Differences, are expected to yield high errors, suggesting the development of alternative approaches and (2) the algorithm for the change of state has the largest impact on the anisotropic influence of the grid. Alternative approaches, such as the decentered square algorithm, may lead to considerable improvement in simulation quality.

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