Application of generalized finite difference method in numerical modelling of moving boundary problems

• Autorzy: Mochnacki B. , Lara S.
• Języki publikacji: EN

Abstrakty

EN

The application of generalized finite difference method for numerical modelling of thermal processes proceeding in the solidifying casting domain is presented. The solidification of pure metals and eutectic alloys is considered. In such case the solidification process takes place at the constant temperature (the Stefan problem). From the numerical point of view the solution of this task is very complex; in particular, in the case of 2D or 3D domains; and in literature one can find the procedures enabling to avoid the difficulties with the direct modelling of the problem discussed. The part of them consist in the substitution of the solidification point T* by the certain interval [T* - ΔT, T* + ΔT]. In this way the subdomain of artificial mushy zone is introduced and the fixed domain approach [1] can be used. On the stage of numerical algorithm construction and numerical simulation the generalized finite difference method is used. In the final part of the paper the examples of computations are shown.

Słowa kluczowe

EN

generalized finite difference method; numerical modelling; thermal processes; solidifying casting; Stefan problem; foundry processes

PL

uogólniona metoda elementów skończonych; modelowanie numeryczne; zagadnienie Stefana; procesy odlewania; procesy cieplne

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
• Rocznik: 2003
• Tom: Vol. 2, nr 1
• Strony: 129--143
• Opis fizyczny: Bibliogr. 7 poz., rys.

Twórcy

autor

Mochnacki B.

• Czestochowa University of Technology, Czestochowa

autor

Lara S.

• Czestochowa University of Technology, Czestochowa

Bibliografia

• [1] Mochnacki B., Suchy J.S., Numerical methods in computations of foundry processes, PFTA, Cracow 1995.
• [2] Hong C.P., Umeda T., Kimura Y., Numerical models for casting solidification problems, Metal. Trans. 1984, 15B, 101-105.
• [3] Lara S., Application of generalized finite difference method in numerical modelling of moving boundary problems, Doctoral thesis, Częstochowa 2003.
• [4] Hsiao J.S., An efficient algorithm for finite-difference analyses of heat transfer with melting and solidification, Numerical Heat Transfer 1985, 8, 653-666.
• [5] Mochnacki B., Pawlak E., Lara S., Numerical solution of 2D Stefan problem, Solidification of Metals and Alloys 2000, 2, 44, 235-238.
• [6] Mochnacki B., Enthalpy approach in numerical modelling of solidification, Part 1, Zeszyty Naukowe Politechniki Opolskiej 2002, Mechanika.
• [7] Mochnacki B., Pawlak E., Lara S., Enthalpy approach in numerical modelling of solidification. Part 2, Zeszyty Naukowe Politechniki Opolskiej 2002, 288, Mechanika z. 75, 133-136.

Uwagi

EN

The papers have been presented during the session devoted to application of mathematics (as part of International Conference on Parallel Processing and Applied Mathematics).