An efficient time-stepping scheme for numerical simulation of dendritic crystal growth. Issue 6 (1st November 2016)

• Record Type: Journal Article
• Authors: Shah, Abdullah; Sabir, Muhammad; Bastian, Peter
• Is Part Of: Revue Européenne de mécanique numérique. Volume 25:Issue 6(2016)
• Page Start: 475
• Page End: 488
• Publication Date: 2016-11-01
• Subjects: Dendritic crystal growth -- phase-field model -- diagonally implicit fractional step -scheme -- conforming finite element method; Engineering mathematics -- Periodicals; Mechanics -- Data processing -- Periodicals; Finite element method -- Periodicals; Mechanics -- Mathematical models -- Periodicals; Engineering -- Statistical methods -- Periodicals; 621.05
• DOI: 10.1080/17797179.2016.1276395
• Languages: English
• ISSNs: 1779-7179

Abstract

Abstract : In this article, we present an adaptive time-stepping technique for numerical simulation of dendritic crystal growth model. The diagonally implicit fractional step -scheme for time discretisation and conforming 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.