Efficient Space-time FE for a Simplified Thermo-metallurgical Problem Relevent to Casting
Conference contribution, 2005

Solving the non-linear thermo-metallurgical problem such as the thermal cooling of a molten metal or the macro-segregation during a cooling process are problems that needs careful consideration. The strong non-linearities of the problem makes it difficult to solve without having a prohibitive high cost arising from the high spatial and time-domain discretization needed to solve the problem. For the studied application of design optimization of cast components a low computational time is important since a lot of computations are necessary in an optimization. From the first law of thermodynamics we derive a space-time FE-discretization for a hierarchy of discontinuous Galerkin in time, dG(k) k>=0. This formulation integrates the stored energy exact. As a special case we regain the enthalpy-method with suitable average of the energy generation over time. For the macro-segregation, the problem is reformulated so that the phase-transition drives a flow of species. Diffusion is possible throughout the domain in this model. This can then be further rewritten using a potential approach. We can by this aproch arrive in discretizations that guaranties that the balance equation is satisfied and can solve phase-transition problem as a field problem or as a local problem. The coupled problems of cooling-transformation are solved. The possibility of using adaptivity in space-time for the coupled problem is discussed.


Andreas Holmström

Chalmers, Applied Mechanics, Material and Computational Mechanics

Fredrik Larsson

Chalmers, Applied Mechanics, Material and Computational Mechanics

Kenneth Runesson

Chalmers, Applied Mechanics, Material and Computational Mechanics

Stefan Edlund

Computational Methods for Coupled Problems in Science and Engineering, COUPLED PROBLEMS 2005 Santorini Island, Greece, May 25-27, 2005


Subject Categories

Mechanical Engineering



More information