A stabilized term-by-term finite element formulation for incompressible liquid–solid phase-change flows

Purpose This paper aims to propose a stabilized finite element formulation for the simulation of incompressible liquid–solid phase-change processes involving natural convection and temperature-dependent thermophysical properties. The formulation addresses the numerical challenges arising from the coupling between momentum and energy equations, the presence of a mushy interface and the nonlinear dependence of material properties on temperature. Design/methodology/approach The formulation is built upon the variational multiscale (VMS) framework with a nonresidual term-by-term stabilization strategy, tailored for fixed-mesh (enthalpy–porosity) methods using the Carman–Kozeny permeability model. The approach enhances stability and ensures optimal dissipation while maintaining accuracy in convection-dominated regimes. The governing equations incorporate temperature-dependent properties and are solved in both two- and three-dimensional configurations. Time integration is performed using a second-order backward differentiation formula. The methodology is validated against well-established experimental benchmarks, including natural convection in air with variable properties and the classical water-freezing problem, and subsequently applied to the passive thermal management of lithium-ion batteries and electronic systems. Findings The results demonstrate that the proposed formulation accurately predicts the evolution of melting and solidification fronts, temperature fields and flow structures without exhibiting spurious oscillations or excessive numerical diffusion. The method effectively captures the nonlinear interaction between latent and sensible heat, preserving stability even under pronounced buoyancy and phase-change coupling effects. Comparisons with experimental data confirm the robustness and predictive accuracy of the formulation. Originality/value In contrast to conventional residual-based stabilization techniques, the present nonresidual VMS formulation introduces only the essential stabilization terms while maintaining robustness and accuracy. The proposed approach provides a reliable and computationally efficient framework for modeling phase-change materials in thermally coupled systems, offering a rigorous and general methodology for energy storage and passive thermal management applications.