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Multi‐grid solution of two coupled Stefan equations arising in induction heating of large steel slabs
Author(s) -
Hoppe Ronald H. W.,
Kornhuber Ralf
Publication year - 1990
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.1620300414
Subject(s) - discretization , slab , grid , spacetime , system of linear equations , mathematics , induction heating , finite difference , type (biology) , mathematical analysis , mechanics , physics , geometry , structural engineering , engineering , electromagnetic coil , geology , paleontology , quantum mechanics
Induction heating of large steel slabs can be described by a coupled system of non‐linear evolution equations of Stefan type represnting the temporal and spatial distribution of the induced magnetic field and the generated temperature within the slab. Discretizing these equations implicitly in time and by finite differences in space, at each time step the solution of a system of difference inclusions is required. For the solution of that system two multi‐grid algorithms are given which, combined with a nested iteration type continuation strategy to proceed in time, result in computationally highly efficient schemes for the numerical simulation of the induction heating process.