期刊
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
卷 19, 期 7, 页码 2309-2323出版社
ELSEVIER SCIENCE BV
DOI: 10.1016/j.cnsns.2013.11.016
关键词
Phase-field; Solidification; Time integration; Nonlinear stability; Structure preservation
类别
资金
- Spanish Ministry of Science and Innovation [DPI2009-14305-C02-02, DPI2012-36429]
- Xunta de Galicia [09REM005118PR, 09MDS00718PR]
- Ministerio de Ciencia e Innovacion [DPI2009-14546-C02-01, DPI2010-16496]
- FEDER funds
- Universidad de A Coruna
A discretization is presented for the initial boundary value problem of solidification as described in the phase-field model developed by Penrose and Fife (1990) [1] and Wang et al. (1993) [2]. These are models that are completely derived from the laws of thermodynamics, and the algorithms that we propose are formulated to strictly preserve them. Hence, the discrete solutions obtained can be understood as discrete dynamical systems satisfying discrete versions of the first and second laws of thermodynamics. The proposed methods are based on a finite element discretization in space and a midpoint-type finite-difference discretization in time. By using so-called discrete gradient operators, the conservation/entropic character of the continuum model is inherited in the numerical solution, as well as its Lyapunov stability in pure solid/liquid equilibria. (C) 2013 Elsevier B. V. All rights reserved.
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