A comparison of methods for the calculation of interface curvature in two-dimensional cellular automata solidification models
| Autor: | Markus Rettenmayr, Klemens Reuther |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Level set method
General Computer Science Interface (Java) Mathematical analysis Finite difference General Physics and Astronomy 02 engineering and technology General Chemistry 010402 general chemistry 021001 nanoscience & nanotechnology Curvature 01 natural sciences Cellular automaton 0104 chemical sciences Moore neighborhood Computational Mathematics symbols.namesake Von Neumann neighborhood Mechanics of Materials Taylor series symbols General Materials Science 0210 nano-technology Mathematics |
| Zdroj: | Computational Materials Science. 166:143-149 |
| ISSN: | 0927-0256 |
| DOI: | 10.1016/j.commatsci.2019.04.050 |
| Popis: | Four methods for the calculation of interface curvature in cellular automata models for solidification are evaluated. Three of the methods are based on the level-set interpretation of the solid fraction field and calculate the required spatial derivatives by finite differences or by a Taylor approximation in different neighborhoods. The fourth method is the height function method, an interface reconstruction method based on the row- or columnwise summation of solid fractions. Two benchmark problems are investigated, representative for two types of cellular automata models for solidification where interface cells exist in either Moore or von Neumann neighborhoods of solid cells. For the case of interface cells in the Moore neighborhood of solid cells, the height function method yields the most accurate results, while all level-set based methods exhibit significant numerical scatter. For the case of interface cells existing in the von Neumann neighborhood of solid cells, all methods yield a higher level of numerical scatter. The best curvature calculations for this case are achieved by the height function method and by the level set method with a Taylor approximation in an extended neighborhood. |
| Databáze: | OpenAIRE |
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