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An analysis of solidification problems by the boundary element method
Author(s) -
Zabaras Nicholas,
Mukherjee Subrata
Publication year - 1987
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/nme.1620241006
Subject(s) - boundary element method , discretization , numerical analysis , convolution (computer science) , boundary (topology) , field (mathematics) , mathematics , boundary value problem , finite element method , boundary knot method , mathematical analysis , computer science , engineering , structural engineering , machine learning , artificial neural network , pure mathematics
The problem of interest in this paper is the calculation of the motion of the solid–liquid interface and the time‐dependent temperature field during solidification of a pure metal. An iterative implicit algorithm has been developed for this purpose using the boundary element method (BEM) with time‐dependent Green's functions and convolution integrals. The BEM approach requires discretization of only the surface of the solidifying body. Thus, the numerical method closely follows the physics of the problems and is intuitively very appealing. The formulation and the numerical scheme presented here are general and can be applied to a broad range of moving boundary problems. Emphasis is given to two‐dimensional problems. Comparison with existing semi‐analytical solutions and other numerical solutions from the literature reveals that the method is fast, accurate and without major time step limitations.