An implicit finite element phase-field technique with temperature-dependent properties for liquid-solid interface evolution

Abstract

We present a fully implicit, finite-element phase-field framework for simulating ice–water solidification in both two and three dimensions. Our model couples a modified heat conduction equation with a regularized Ginzburg–Landau phase-field evolution law, explicitly accounting for anisotropic diffusion and temperature-dependent constitutive properties (density, specific heat and thermal conductivity). After verifying accuracy on a classical 2D undercooling benchmark, we carry out systematic parametric studies to assess the effects of time-step size and mesh resolution on interface dynamics. Three demonstrative cases—two in 2D and one in 3D—show that dendritic morphologies emerge naturally on uniform meshes, without any special adaptive remeshing. We further quantify how temperature-dependent parameters accelerate mid-stage growth kinetics. The proposed approach combines robustness, versatility and computational efficiency, and is released alongside documented Mathematica/AceGen source code to support reproducibility and further extensions.