On a numerical model for diffusion-controlled growth and dissolution of spherical precipitates (Q1272376)

Summary: This paper deals with a numerical model for the kinetics of some diffusion-limited phase transformations. The governing equations are the diffusion equation (second Fick's law) for the concentration of dissolved element in the matrix, with a known value at the precipitate-matrix interface, and the flux balance (first Fick's law) at this interface. The numerical method, outlined for this free boundary value problem, is based upon a fixed domain transformation and a suitably adapted nonconforming finite element technique for the space discretization. The algorithm can be implemented on a PC. By numerous experiments the method is shown to give accurate numerical results.