A thermodynamically consistent numerical method for a phase field model of solidification |
| |
| Institution: | 1. E.T.S.I. Industriales, Technical University of Madrid, José Gutiérrez Abascal 2, 28006 Madrid, Spain;2. Department of Mathematical Methods, Universidade da Coruna, Campus de Elviña s/n, 15192 A Coruña, Spain;1. Department of Mathematics, University of Dundee, Dundee, DD1 4HN, Scotland, United Kingdom;2. Department of Applied Mathematics and Mechanics, University of Science and Technology Beijing, Beijing 100083, China;3. Department of Mathematics, University of California, Irvine, CA 92697, USA;1. Australian Research Council Centre of Excellence for Core to Crust Fluid Systems/GEMOC, Department of Earth and Planetary Sciences, Macquarie University, Sydney, Australia;2. Laboratori de Càlcul Numèric, Escola Tècnica Superior d’Enginyers de Camins, Canals i Ports, Universitat Politècnica de Catalunya, Barcelona, Spain;9. Faculty of Civil Engineering, Duy Tan University, Da Nang, 550000, Viet Nam |
| |
| Abstract: | 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. |
| |
| Keywords: | Phase-field Solidification Time integration Nonlinear stability Structure preservation |
| 本文献已被 ScienceDirect 等数据库收录！ |
|
