An efficient time-stepping scheme for numerical simulation of dendritic crystal growth

In this article, we present an adaptive time-stepping technique for numerical simulation of dendritic crystal growth model. The diagonally implicit fractional step theta-scheme for time discretisation and conforming Q1 finite-element method for space discretisation are used. The performance of the scheme is illustrated by simulating two-dimensional dendritic crystal growth problem, allowing the comparison with other numerical methods. In addition, traditional diagonally implicit Runge-Kutta method is used and comparison is given with the proposed scheme. Robustness is observed for the present scheme. Parametric effects on the growth and shape of dendrites are also given.