Phase transition simulations for solidification of fe-c alloy with cellular automata interfaced with self-adaptive hp finite element method for non-stationary heat and mass transport problems

Maciej Paszyński¹ , Jerzy Gawąd², Paweł Matuszyk², Łukasz Madej², Dorota Podorska³

¹Department of Computer Science, AGH University of Science and Technology, Al. Mickiewicza 30, 30-059 Krakow, Poland. ²Department of Applied Computer Science and Modelling, AGH University of Science and Technology, Al. Mickiewicza 30, 30-059 Krakow, Poland. ³Department of Ferrous Metallurgy, AGH University of Science and Technology, Al. Mickiewicza 30, 30-059 Krakow, Poland.

DOI:

https://doi.org/10.7494/cmms.2008.4.0256

Abstract:

The simulation of the phase transition for solidification of Fe-C alloy with the Cellular Automata (CA) method interfaced with the hp-adaptive Finite Element Method (FEM) for the non-stationary heat and mass transport problems is presented in the paper. The computational domain is discretized by the uniform grid for the CA and a sequence of non uniform meshes for the self-adaptive hp-FEM. The rule-based CA model is responsible for the simulation of the grow of the new phase within the Fe-C alloy. The self-adaptive hp-FEM generates a sequence of meshes delivering exponential convergence of the numerical error with respect to the mesh size (CPU time). The solution from the previous time step as well as material data from the CA grid are projected to the current self-adaptive hp-FEM. The detailed description of the developed approach as well as the examples of numerical simulations are presented and discussed in the paper.

Cite as:

Paszyński, M., Gawąd, J., Matuszyk, P., Madej, Ł., & Podorska, D. (2008). Phase transition simulations for solidification of fe-c alloy with cellular automata interfaced with self-adaptive hp finite element method for non-stationary heat and mass transport problems. Computer Methods in Materials Science, 8(4), 179 – 185. https://doi.org/10.7494/cmms.2008.4.0256

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