Numerically Stable Computer Simulation of Solidification: Association Between Eigenvalues of Amplification Matrix and Size of Time Step

Abstract

The constantly increasing demand for efficient and precise computational solvers becomes the crucial factor deciding about usability of a given domain specific simulation software. The main idea of this article is the use of eigenvalues of amplification matrices to determine the size of time step in modeling of solidification. As far as numerical simulations are concerned it is very important to obtain solutions which are stable and physically correct. It is acquired by fulfilling many assumptions and conditions during the construction a numerical model and carrying out computer simulations. One of the conditions is a proper selection of time step. The size of time step has a great impact on the stability of used time integration schemes (e.g. explicit scheme), or on a proper image of physical phenomena occurring during the simulation (e.g. implicit scheme). The eigenvalues of amplification matrix in governing equations influence on the appropriate selection of size of time step in computer simulations. Hence, it allows to better fit the size of time step and time integration scheme for modeled structure.