Space-time finite elements for a simplified thermo-metallurgical problem relevant to casting
Journal article, 2007

The non-linear thermo-metallurgical problem, relevant for the cooling of a molten metal including the macro-segregation that occurs during the cooling process, is studied here. Due to the strong non-linearities involved in phase transformations, it is necessary to use a fine resolution in space-time in a finite element approximation in order to meet accuracy requirements. We derive space-time FE-methods based on the discontinuous and continuous Galerkin method in time for the energy equation. This formulation integrates the stored energy exactly for a given heat flux. When macro-segregation is incorporated into the model, the problem can be formulated in such a way that the phase-transition drives a flow of species. In addition, diffusion is possible throughout the domain. The model can be further rewritten using a potential approach. By this approach for modelling macro-segregation, we are able to obtain discretizations that guarantee that the balance equations are satisfied, and it is possible to solve the phase-transition problem either as a field problem or as a local problem (defined by a local evolution rule). © Springer Verlag 2007.


Andreas Holmström

Fredrik Larsson

Chalmers, Applied Mechanics, Material and Computational Mechanics

Kenneth Runesson

Chalmers, Applied Mechanics, Material and Computational Mechanics

Computational Mechanics

0178-7675 (ISSN) 1432-0924 (eISSN)

Vol. 40 2 341-353

Subject Categories

Mechanical Engineering



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