Conservative formulations for heat transfer simulation with sharp interfaces and discontinuous properties in two-phase flows

In this article, innovative formulations in the finite volume framework are proposed to tackle the thermal energy loss numerical issue in two-phase flow simulations with sharp interface and discontinuous properties, independently from the flow dynamics. The conservation of the formulation depends on several choices: the way the temperature equation is written and integrated, the hypothesis on the fluxes due to the discontinuity of the physical properties, and the space and time discretizations. After a presentation of the numerical methods considered in this study, a fully three-dimensional case is presented. At first the simulation only includes diffusion, and the convergence is quite good with the improvement proposed. Then, the drawbacks of the usage of one-fluid formulation with diffusion and convection are highlighted and characterized depending on the mesh size. Finally, several sets of coherent choices, named as formulations, are proposed and a genuinely conservative formulation with good abilities to predict the temperature is found and tested in a representative one-dimensional case.