Interface Retaining Coarsening of Multiphase Flows

TL;DR

This paper presents a method for coarsening multiphase flow simulations while preserving sharp interfaces, enabling reduced models to accurately capture interface dynamics and flow behavior.

Contribution

It introduces a novel interface retaining coarsening technique that combines diffusion-based phase identification with interface tracking for multiphase flows.

Findings

Method effectively retains sharp interfaces during coarsening.

Coarse model results closely match fully resolved simulations in Rayleigh-Taylor instability.

Demonstrates potential for improved reduced order modeling of multiphase flows.

Abstract

Multiphase flows are characterized by sharp moving interfaces, separating different fluids or phases. In many cases the dynamics of the interface 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. Here, a process to coarsen or filter fully resolved numerical solutions for incompressible multiphase flows while retaining a sharp interface is examined. The different phases are identified by an index function that takes different values in each phase and is coarsened by solving a constant coefficient diffusion equation, while tracking the interface contour. Small flows 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, plus a pressure like equation to enforce incompressibility of the coarse velocity field. Examples of different levels of coarsening are shown. A simulation of a coarse model, where small scales are treated as a homogeneous mixture, results in a solution that is similar to the filtered fully resolved field for the early time Rayleigh-Taylor instability.