Fully Decoupled Fractional-Step Methods for Non-Linear Viscoelastic Flows: Natural Heat Convection, Viscous Dissipation and Phase Change

This article proposes an accurate splitting method for thermally-coupled incompressible flow problems involving nonlinear viscoelastic fluids. Our technique uses a semi-implicit reformulation of the system to, at each time step, efficiently decouple all the individual sub-problems (velocity, pressure, stresses, temperature). Further attractive features of our framework are its high-order accuracy and complete flexibility regarding the choice of viscoelastic constitutive model. We assess the method with the differentially-heated square cavity, incorporating viscous dissipation and an enthalpy-based phase-change model. Our numerical tests consider PTT and FENE-P fluids, combined, for the first time, with a phase-change model. Rayleigh numbers between 103 and 105 and Weissenberg numbers up to 10 are tested. We investigate the influence of different flow parameters on the hydrodynamic and thermal boundary layer patterns. Average Nusselt number values are validated with reference results, and new results are presented to guide future works. We include qualitative velocity, temperature and stress results. Our method captures the details of natural convection and phase-change cycles, including steady and time-dependent scenarios. The results comprehensively describe the fluid flow and the solid–liquid–solid phase-change cycle within the cavity, providing valuable insights into these complex phenomena. © 2025 Elsevier B.V.