Abstract
The goal of the paper is to review and compare two of the most popular methods for modeling the dendritic solidification in 2D, that tracks the interface between phases implicitly, e.g. the phase-field method and the level set method. We apply these methods to simulate the dendritic crystallization of a pure melt. Numerical experiments for different anisotropic strengths are presented. The two methods compare favorably and the obtained tip velocities and tip shapes are in good agreement with the microscopic solvability theory.
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References
Juric, D., Tryggvason, G.: A front tracking method for dendritic solidification. J. Comput. Phys. 123, 127–148 (1996)
Karma, A., Rappel, W.-J.: Phase-field method for computationally efficient modeling of solidification with arbitrary interface kinetics. Phys. Rev. E 53, 3017–3020 (1996)
Karma, A., Rappel, W.-J.: Quantitative phase-field modeling of dendritic growth in two and three dimensions. Phys. Rev. E 57, 4323–4349 (1998)
Slavov, V., Dimova, S., Iliev, O.: Phase-field method for 2D dendritic growth. In: Pires, F.M., Abreu, S.P. (eds.) EPIA 2003. LNCS (LNAI), vol. 2902, pp. 404–411. Springer, Heidelberg (2003)
Slavov, V., Dimova, S.: Phase-field modelling of dendritic interaction in 2D. Mathematics and Education in Mathematics 2902, 466–471 (2004)
Osher, S., Sethian, J.A.: Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi Formulations. J. Comput. Phys. 79, 12–49 (1988)
Jiang, G.-S., Peng, D.: Weighted ENO schemes for Hamilton-Jacobi equations. SIAM J. Sci. Comput. 21, 2126–2143 (2000)
Chen, S., et al.: A simple level set approach for solving Stefan problems. J. Comput. Phys. 135, 89–112 (1997)
Gottlieb, S., Shu, C.-W., Tadmor, E.: Strong stability-preserving high-order time discretization methods. SIAM Review 43, 89–112 (2001)
Novikov, V., Novikov, E.: Stability control of explicit one-step methods for integration of ordinary differential equations. Dokl. Akad. Nauk SSSR 272, 1058–1062 (1984)
Gibou, F., et al.: A Level set approach for the numerical simulation of dendritic growth. J. Sci. Comput. 19, 183–199 (2003)
Kim, Y., Goldenfeld, N., Dantzig, J.: Computation of dendritic microstructures using a level set method. Phys. Rev. E 62, 2471–2474 (2000)
Peng, D., et al.: A PDE-based local Level set method. J. Comput. Phys. 155, 410–438 (1999)
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Slavov, V., Dimova, S. (2007). Phase-Field Versus Level Set Method for 2D Dendritic Growth. In: Boyanov, T., Dimova, S., Georgiev, K., Nikolov, G. (eds) Numerical Methods and Applications. NMA 2006. Lecture Notes in Computer Science, vol 4310. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70942-8_87
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DOI: https://doi.org/10.1007/978-3-540-70942-8_87
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-70940-4
Online ISBN: 978-3-540-70942-8
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