Simulation of Morphological Changes of Solid Bodies with an Arbitrary Shapes Subjected to Thermal Treatment
M. Talbi*, S. Ramdani, M. Benkaddour
Laboratoire d'Analyse et de Caractérisation des Matériaux,
* Corresponding author. E-mail :firstname.lastname@example.org
Received : 02 November 2001; revised version accepted :02 February 2002
In this paper, we develop a numerical schemes to model the surface evolution of an isotropic crystal of arbitrary shape due to surface diffusion, possibly in combination with free evaporation. This study is based on phenomenological approach. It comprises two phases : a phase which establish the analytical equation describing the morphological evolution driven by mean curvature gradient and a phase of simulation which resolves this equation. The numerical resolution of equation obtained, which includes a fourth derivation term, is based on two approximations : the bspline methods to approach the surface of the studied form through a set of points in order to calculate the different partial derivatives, and the finite difference methods according to temporal variable, to know the morphological evolution during time. An algorithm is proposed and the numerical resolution is applied on some geometric shapes.
Keywords : Surface; Diffusion; Evaporation; Numerical resolution; Bspline.