Solution of a phase-field model for dissolution of primary particles in binary aluminum alloys by an r-adaptive mesh-free method

The dissolution of primary particles in homogenization of binary aluminum alloys is simulated by the phase-field model. The driving force for the phase transformation is obtained by the JMatPro software. The diffusion-controlled dissolution of Al3Mg2 particle in aluminum is first solved by the phase-field model and the classical front-tracking model for comparison purposes. Both models are solved by the finite-difference method. The results show excellent agreement between the two different physical models. An advanced mesh-free numerical procedure based on the local radial basis function collocation method is presented for more advanced solving of the phase-field model. The method is implemented with an elliptic automatic adaptive node redistribution to properly cope with the diffuse interface gradients and to simultaneously reduce the number of required nodes. The numerical results are compared with the fine-grid finite-difference method reference results. Excellent agreement is obtained which proves the suitability of the developed new adaptive mesh-free solution procedure for coping with the phase-field model.