Leapfrog/Dufort-Frankel explicit scheme for diffusion-controlled moving interphase boundary problems with variable diffusion coefficient and solute conservation

Abstract

A new numerical model with solute conservation is developed to study diffusion-controlled interphase-interface migration kinetics. The new model which can directly incorporate variable and constant diffusion coefficients is a fully explicit numerical method based on Leapfrog and Dufort-Frankel’s explicit schemes. The stability and consistency analysis of this model show that applying the Leapfrog/Dufort-Frankel scheme to Landau transformed Fick’s second law problem, results in a more stable solution that ensures computational accuracy and enhances the computation efficiency when compared to the classical explicit model. The new explicit model is more accurate, direct and faster than implicit models because it does not involve non-trivial assumptions that decrease the accuracy of implicit models. This model is used in this work to modify the classical Heckel’s criteria for second-phase growth, to predict factors that affect the growth rate, homogenization time, and the extent of second-phase growth, in a two-phase alloy.