### Abstract

A simple two-dimensional model for the solidification of a “warm” solid seed placed in an under cooled liquid melt is presented. Under the physically restrictive assumptions of no surface anisotropy or curvature and kinetic under-cooling a closed form similarity solution can be constructed for this problem. A fixed grid enthalpy “like” solution can also be constructed. When this enthalpy solution is implemented in a one-dimensional cylindrical geometry it produces excellent agreement with the analytical solution. When implemented in a two-dimensional geometry, however, due to the lack of front stability provided by the surface under-cooling, dendritic crystals are predicted. Theses crystals are referred to as “numerical crystals” to highlight the fact that they are a pure artefact of the anisotropies introduced by the grid, and the initialization and operation of the proposed numerical method. The paper closes by suggesting that the proposed analytical solution, although not physically complete, is a rigorous and hard test for the quality of a given crystal growth algorithm, since an “ideal” two-dimensional numerical method should be able to recover the cylindrical growth of the seed without forming dendrites.

Original language | English (US) |
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Pages (from-to) | 322-325 |

Number of pages | 4 |

Journal | International Conference on Computational Methods for Thermal Problems |

Issue number | 223599 |

State | Published - Jan 1 2009 |

Event | 1st International Conference on Computational Methods for Thermal Problems, THERMACOMP 2009 - Naples, Italy Duration: Sep 8 2009 → Sep 10 2009 |

### Keywords

- Crystal growth
- Enthalpy method
- Similarity solution

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## Cite this

*International Conference on Computational Methods for Thermal Problems*, (223599), 322-325.