The correlation between the eigenvalues of global FEM matrix and the size of time step in the numerical solutions of solidification equation

• Autorzy: Zych M.
• Języki publikacji: EN

Abstrakty

EN

In the paper the influence of the eigenvalues of the matrix on the stability of the numerical simulations of binary alloy solidification process was analyzed. One step Θ scheme time integration for the modeling was used. The occurrence of the equation clotting full, diagonal and lumped capacitance matrix was considered. In the explicit schema (conditionally stable) the major influence on the proper selection of the size of the critical time step was proved. The physically incorrect results are given when the maximum allowable time step is exceeded.

Słowa kluczowe

EN

eigenvalues of the matrix; time step; numerical stability; solidification

PL

czas końcowy; stabilność numeryczna; krzepnięcie

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2014
• Tom: Vol. 13, nr 3
• Strony: 201--206
• Opis fizyczny: Bibliogr. 6 poz.

Twórcy

autor

Zych M.

• Institute of Computer and Information Science, Czestochowa University of Technology Częstochowa, Poland

Bibliografia

• [1] Sczygiol N., Modelowanie numeryczne zjawisk termomechanicznych w krzepnącym odlewie i formie odlewniczej, Wydawnictwo Politechniki Częstochowskiej, Częstochowa 2000.
• [2] Sczygiol N., Szwarc G., Application of enthalpy formulations from numerical simulation of castings solidification, Computer Assisted Mechanics and Engineering Sciences 2011, 8, 99-120.
• [3] Shen R.Wu, Lumped mass matrix in explicit finite element method for transient dynamics of elasticity, Comput. Methods Appl. Mech. Engrg. 2006, 195, 5983-5994.
• [4] Gawrońska E., Sczygiol N., Stability of the mixed time partitioning methods in relation to the size of time step, Special Issue: 82nd Annual Meeting of the International Association of Applied Mathematics and Mechanics (Gesellschaft für Angewandte Mathematik und Mechanik), GAMM 2011, 18-21 April 2011, Graz, Austria, 467-468.
• [5] Gawrońska E., Sczygiol N., Application of mixed time partitioning methods to raise the efficiency of solidification modeling, 12th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, SYNASC 2010, 23-26 September 2010, Timisoara, Romania, 99-103.
• [6] Wood W.L., Partical Time-stepping Schemes, Clarendon Press, Oxford 1990.