Large Eddy Simulation (LES) for Multiphase Flows based on Interface Retaining Coarsening

Large Eddy Simulation (LES), where the unsteady motion of the large scales is simulated and models are used to describe the average motion of the small scales, is a promising way for predicting the dynamics of single phase flow. It is likely that a similar strategy is useful for multiphase, but not in a conventional way. For multiphase flows where sharp moving phase boundaries separate different fluids or phases, the dynamics of the interface often determines the behavior of the flow. In a coarse, or reduced order model, it may therefore be important to retain a sharp interface for the resolved scales, in a similar way that modeling of disperse flows often retain bubbles or drops as point particles. We describe a systematic process to coarsen fully resolved numerical solutions for multiphase flows while retaining a sharp interface. The different phases are identified by an index function that takes different values in the different phases and is coarsened by solving a constant coefficient diffusion equation, while tracking the interface contour. Small flow scales of one phase, left behind when the interface is moved, are embedded in the other phase by solving another diffusion equation with a modified diffusion coefficient that is zero at the interface location to prevent diffusion across the interface, along with a pseudo pressure equation to preserves the incompressibility of the coarsened volumetric velocity field. Several examples of different levels of coarsening are shown. The dynamics of the small scales in the mixed regions can be modeled in many different ways, including using homogeneous mixture, drift flux, and two fluid Euler-Euler models, as well as Euler-Lagrange models. We are currently applying simple homogeneous mixture model and the evolution equation for the coarsened flow field is derived. Those subgrid terms are determined based on machine learning and preliminary results of predictions for the closure terms on a 2D jet are shown.