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

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.