A novel liquid fraction iteration methodology for addressing oscillatory issues in the total enthalpy method

The total enthalpy method (TEM) has been proposed and employed for several decades to address both isothermal and gradual phase change problems. However, recent investigations into isothermal phase changes have revealed that the phase interface predicted by the TEM oscillates with variations in spatial and temporal discretizations, due to the inconsistency between liquid fraction and enthalpy. To address this issue, and drawing inspiration from the liquid fraction iteration methodology used in the widely adopted heat source method (HSM) to ensure consistency between liquid fraction and temperature, this paper introduces a novel liquid fraction iteration methodology specifically tailored for the TEM, referred to as the iterative TEM (ITEM). This approach is validated against an experimental benchmark involving the melting of a pure substance. Grid and time-step dependence studies confirm that the ITEM effectively eliminates oscillations and exhibits convergence with respect to both grid size and time step. Moreover, the ITEM achieves accuracy comparable to that of the HSM. Finally, the computational costs associated with the ITEM are examined, revealing that costs increase rapidly once the grid Fourier number (Fo) exceeds one. Maintaining the grid Fo number below approximately 0.5 and ensuring the ratio of the relaxation factor to the grid Fo number to approach one significantly improve computational efficiency. The relaxation factor is a crucial parameter within the liquid fraction iteration scheme.