A Convergence Study of the One-Fluid Formulation in a Phase Inversion Application at Moderate Reynolds and Weber Numbers

As a consequence of the remarkable advances in computational sciences realized over the past decades, complex physical processes can now be simulated. To insure fidelity and accuracy, precise convergence criteria must be satisfied. While efforts have been dedicated towards the validation of the computational tools specialized in two-phase flows, there remains a number of open questions. One of them is whether numerical solvers build upon the one-fluid formulation are able to converge integral quantities. This includes enstrophy, to which the boundary layers that develop in the interface vicinity contribute the most. A subsequent question is whether the lack of convergence of the aforementioned quantity affects lower order statistics, chief among them the surface area density. The presented work examines these questions in the context of the phase inversion configuration [1, 2]. Moderate Reynolds and Weber numbers are selected so as to guarantee proper resolution of the single-phase flow. The simulations are performed using Basilisk, a recently developed tree-based software using adaptive meshes.