# Dissertation: 18.12. Efficient numerical methods for simulating continuous casting processes (Räisänen)

Start date: Dec 18, 2014 12:00 AM

End date: Dec 18, 2014 03:00 PM

Location: Mattilanniemi, Agora Auditorio 2

Lic.Ph. Tuomo Räisänen defends his doctoral dissertation in Information Technology ”Efficient numerical methods for simulating continuous casting processes”. Opponent Adjunct Professor Erkki Laitinen (University of Oulu) and custos Professor Timo Tiihonen (University of Jyväskylä). The event is in Finnish.

The dissertation has been published in the series Jyväskylä studies in Computing, number 210, ISSN 1456-7390, ISBN 978-951-39-6014-8, ISBN 978-951-39-6013-1. It is available at the University Library’s Publications Unit, tel. +358 40 805 3825, myynti@library.jyu.fi.

### Abstract:

This study considers modeling, approximating, and simulating of continuous casting processes.

The focus is especially on the numerical efficiency of methods. We approach the casting processes using enthalpy based modeling. This leads to a three-dimensional transient convection dominated two-phase Stefan problem with the nonlinear boundary condition. Under suitable assumptions the problem is mathematically well posed. We introduce a three-dimensional model and show qualitative properties.

Fully discrete Galerkin approximation of the model leads to a large-scale nonlinear discrete problem for which the convection dominance also causes stability issues. To overcome these, we apply the method of characteristics and the upwinding technique.

Furthermore, we are able to apply so-called nonlinear Chernoff formula to these approximations and, as a result, the discrete approximated  model can be solved  using only  linear algebraic equations at each time step.

All together, we consider four different approximations. We show their convergence and describe the implementation using matrix formulations. By solving a numerical example, we compare approximations in terms of the rate of convergence and solution time.

Finally, we study how the presented approximations perform on an industrial scale. For this purpose, we use an artificial machine producing stainless steel to get an example of a detailed model and realistic computational challenges.

We discuss the changes in the solution algorithms compared to the model problem and introduce an efficient solution algorithm. We validate our software, compare our approximations, and make conclusions about the numerical efficiency.

• Further information:

Tuomo Räisänen, tuomo.raisanen@mit.jyu.fi, puh. 040 734 5200
Communications officer Anitta Kananen, tiedotus@jyu.fi, puh. 040 805 4142

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