Coordinate transformation techniques.
Here the unknown is mapped onto a regular geometrical region. The A 2D axisymmetric formulation for the solution of a directional solidification problem using an inverse finite-element method resulting transformed equations are then solved on this (IFEM) is presented. An algorithm developed by A. N. Alexandrou domain using N ฯช 1 of the N boundary conditions. The (Int. J. Numer. Methods Eng. 28, 2383, 1989) has been modified Nth condition, sometimes referred to as the distinguished and extended to include more general boundary conditions. The condition [1] is used to determine the location of the free latter includes the explicit presence of an ampoule (with a complex or moving boundary in physical space in an iterative fashshape) that contains the solid and the melt from which it is growing. Heat transfer between the ampoule and the external environment, ion. This approach has been realized, using different solutime-dependent thermal boundary conditions, nonmonotonic temtion techniques, including finite element [2-5] and, reperature distributions, and species diffusion in the melt and crystal cently, Chebyshev spectral techniques [6]. The techniques are also taken into account. Thus, our extended formulation encomemployed to handle the mapping include Landau-type passes a wider class of solidification problems than previous IFEM transformations [6, 7] and numerically generated moving methods. Numerical experiments that illustrate the suitability of the extended IFEM are presented. In particular, we present a simulation orthogonal curvilinear systems obtained by elliptic mesh of the directional solidification of zinc cadmium telluride using generation methods (see, for example, [8]).
boundary conditions corresponding to an actual experiment scenario. แฎ 1997 Academic Press (b) Enthalpy methods. Enthalpy methods, first suggested by Rose [9], are ''fixed domain'' based approaches to phase change problems which do not require explicit this approach have shown that it can successfully reproduce 243