A Hermite radial basis function collocation approach for the numerical simulation of crystallization processes in a channel

摘要

A numerical model of crystal needles growing in a channel from an over-saturated solution is considered. The proposed numerical approach is based on the Hermite radial basis function meshless collocation technique. Numerically, the above phenomenon is very unstable and any small perturbation in the interface shape may give rise to the growth of an artificial (numerical) branch at the crystal interface. Our simulation does not show any evidences of such numerical instabilities and is able to predict the conditions under which real physical interface instabilities are expected. In the numerical algorithm, at each time step of the evolution, we only move the collocation points defining the crystal interface without changing the position of any of the other original collocation points. We are able to carry out this type of scheme due to robustness of the proposed Hermite interpolation approach. In this way, the proposed meshless collocation approach results in a very simple and efficient technique to deal with this type of moving boundary problems.