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.