On the discrete equation model for compressible multiphase fluid flows

TL;DR

This paper revisits and rigorously analyzes the discrete equation method (DEM) for two-phase multiphase flows, establishing its ability to model various flow regimes and proposing a unified PDE framework with key parameters for microstructure uncertainty.

Contribution

The paper introduces a rigorous analysis of DEM's probability coefficients, reformulates it as a one-parameter PDE family, and proposes procedures for equilibrium relaxation, enhancing modeling flexibility.

Findings

DEM can model disperse to stratified flows.

The PDE family interpolates between flow regimes.

Parameters quantify microstructure uncertainty.

Abstract

The modeling of multi-phase flow is very challenging, given the range of scales as well as the diversity of flow regimes that one encounters in this context. We revisit the discrete equation method (DEM) for two-phase flow in the absence of heat conduction and mass transfer. We analyze the resulting probability coefficients and prove their local convexity, rigorously establishing that our version of DEM can model different flow regimes ranging from the disperse to stratified (or separated) flow. Moreover, we reformulate the underlying mesoscopic model in terms of an one-parameter family of PDEs that interpolates between different flow regimes. We also propose two sets of procedures to enforce relaxation to equilibrium. We perform several numerical tests to show the flexibility of the proposed formulation, as well as to interpret different model components. The one-parameter family of PDEs provides an unified framework for modeling mean quantities for a multiphase flow, while at the same time identifying two key parameters that model the inherent uncertainty in terms of the underlying microstructure.