Comparative Analysis of Fixed-Grid Methods in Addressing a Benchmark Problem Coupled Natural Convection and Melting

For decades, the fixed-grid method (FGM) has undergone extensive development and widespread application in addressing phase change problems. Nonetheless, comparative studies on various FGMs in convective regime are considerably scarce. Moreover, it has been proven that two-dimensional (2D) numerical simulations can cause large deviations from experimental observations. Therefore, this study, based on a reference experiment involving gallium melting, seeks to comprehensively and quantitatively compare three prevalent FGMs: enthalpy method (EM), total enthalpy method (TEM), and heat source method (HSM). The TEM validates overestimation of temperature at low Péclet numbers, as the heat dissipation induced by non-uniform thermal properties in solid and liquid phases is not accounted for. To address this issue, a revised TEM has been introduced. The three FGMs were implemented within the OpenFOAM software, with over 150 simulations conducted on 3D meshes. The comparison focused on evaluating the numerical robustness, accuracy and stability of these FGMs, along with exploring their similarities and differences in flow patterns and velocities. Results obtained reveal that EM offers accuracy but lacks robustness, TEM manifests relatively large errors and instability due to oscillation with variations in grid size and time step, while HSM excels in robustness, accuracy, and stability. Under an identical discretization scheme, all FGMs predict similar melt front shapes, vortex structures, and velocity magnitudes. However, with the upwind scheme, the velocity magnitude of the secondary flow is approximately 50 pct of that with high-order schemes, yet it tends to overestimate the melting rate. The reason lies in the limited capacity of the slow secondary flow to effectively disrupt the stable and persistent vortex in the primary flow direction, consequently enhancing heat transfer efficiency in this direction.