2025-06-022025-04Dittler, R. A., Demarchi, M. C., Álvarez-Hostos, J. C., Albanesi, A. E., & Tourn, B. A. (2025). A regularized approach for derivative-based numerical solution of non-linearities in phase change static hysteresis modeling. International Communications in Heat and Mass Transfer, 163, 108691. https://doi.org/10.1016/j.icheatmasstransfer.2025.108691https://hdl.handle.net/20.500.12272/13127Phase change materials (PCMs) represent a promising solution for thermal energy storage (TES) since they can store and release energy in the form of latent heat during solid↔liquid transitions. Nevertheless, accurately simulating the thermal behavior of PCMs remains challenging due to the non-linearities concerning latent heat effects and enthalpy hysteresis. This work introduces a stable and robust procedure based on the finite element method (FEM) under a mixed enthalpy–temperature formulation to address such non-linearities, which enables the numerical solutions using derivative-based algorithms such as the Newton–Raphson (NR) method. The static hysteresis model (SHM) is implemented in the FEM-based formulation via a regularization of the liquid fraction function in response to the sign of the temperature rate. This novel approach ensures a continuous and smooth heating↔cooling transition while retaining the SHM energy-conservative features to properly solve its non-linearities. The method is validated through a one-dimensional benchmark problem, demonstrating high performance and physical fidelity for both complete and partial phase changes. It achieves second-order convergence rates, ensures numerical stability even for large time steps, and maintains accuracy under diverse thermal boundary conditions. Finally, the method is extended to two-dimensional problems, highlighting its robustness and scalability for practical applications in TES systems.pdfeninfo:eu-repo/semantics/embargoedAccessAttribution-NonCommercial 4.0 Internationalhttp://creativecommons.org/licenses/by-nc/4.0/HysteresisRegularizationFinite element methodNewton–RaphsonPhase change materialsEnthalpy–temperature formulationinfo:eu-repo/semantics/articleElsevier B.V.© 2025 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.https://doi.org/10.1016/j.icheatmasstransfer.2025.1086912035-04