Generalization of temporary temperature field correction method in numerical modelling of solidification

The temporary temperature field correction method constitutes a very effective tool for numerical modelling of solidification. The most general version of this algorithm has been presented by Mochnacki [1] and Szopa [2], The basic idea of the method consists in the computations of temperature field for homogeneous domain (e.g. corresponding to molten metal or solid body) and obtained in this way a discrete temperature field for time t is in adequate way 'rebuilt' using the simple mathematical formulae. In this way the non-homogeneous geometry of solidifying casting is taken into account. This approach can be used in the case of macro modelling, in particular when the one domain approach [3, 4, 5, 6] is applied. The basic assumption of the algorithm presented in [ 1 ] and [2] was that the substitute thermal capacity (STC) [7, 8] of casting material can be approximated by a piece-wise constant function. In this paper the generalization of the method on a case of practically optional function describing a course of STC. In the final part of the paper one can find the example of numerical simulations using this approach.

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Metoda poprawiania chwilowego pola temperatury jest bardzo efektywnym narzędziem możliwym do wykorzystania przy modelowaniu procesu krzepnięcia. Przedstawioną w pracach Mochnackiego [1] i Szopy [2] wersję dotyczącą schodkowych zmian zastępczej pojemności cieplnej uogólniono na przypadek funkcji o dowolnym przebiegu.