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A THREE‐DIMENSIONAL FINITE‐VOLUME/NEWTON METHOD FOR THERMAL‐CAPILLARY PROBLEMS
Author(s) -
LAN C. W.,
LIANG M. C.
Publication year - 1997
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/(sici)1097-0207(19970228)40:4<621::aid-nme82>3.0.co;2-5
Subject(s) - jacobian matrix and determinant , finite volume method , finite element method , iterative method , newton's method , capillary action , mathematics , convergence (economics) , generalized minimal residual method , matrix (chemical analysis) , boundary value problem , heat transfer , mathematical analysis , nonlinear system , mechanics , materials science , mathematical optimization , physics , thermodynamics , quantum mechanics , economics , composite material , economic growth
A three‐dimensional finite‐volume/Newton method is developed for solving thermal‐capillary problems in materials processing. The conductive heat transfer, melt–solid interfaces, the melt–gas free surface, and the shape of grown material are calculated simultaneously. The implementation of interface and free surface boundary conditions, as well as co‐ordinate transformation, is described in detail. During the Newton iterations, due to the complexity of the problem, the Jacobian matrix is estimated by finite differences, and the linear equations are solved by the ILU(0) preconditioned GMRES iterative method. Nearly quadratic convergence of the scheme is achieved. Sample calculations for floating‐zone and Stepanov crystal growth are illustrated. © 1997 by John Wiley & Sons, Ltd.