Computationally Efficient and Interface Accurate Dual-Grid Phase-Field Simulation of Turbulent Drop-Laden Flows

In this work, we develop a dual-grid approach for the direct numerical simulations of turbulent multiphase flows in the framework of the phase-field method (PFM). With the dual-grid approach, the solution of the Navier-Stokes equations (flow-field) and of the Cahn-Hilliard equation (phase-field) are performed on two different computational grids. In particular, a base grid - fine enough to resolve the flow down to the Kolmogorov scale - is used for the solution of the Navier-Stokes equations, while a refined grid - required to improve the description of small interfacial structures - is used for the solution of the Cahn-Hilliard equation (phase-field method). The proposed approach is validated, and its computational efficiency is evaluated considering the deformation of a drop in a two-dimensional shear flow. Analyzing the computational time and memory usage, we observe a reduction between ≃30% and ≃40% (with respect to the single-grid approach), depending on the grid refinement factor employed for the phase-field variable. The applicability of the approach to a realistic three-dimensional case is also discussed, by focusing on the breakage of a thin liquid sheet inside a turbulent channel flow. Indications on the grid resolution representing a good compromise between accuracy and computational efficiency in drop-laden turbulence are also provided.