Monolithic Solvers for Incompressible Two-Phase Flows at Large Density and Viscosity Ratios

Mohamed El Ouafa,Stephane Vincent,Vincent Le Chenadec

doi:10.3390/fluids6010023

Abstract

In this paper, we investigate the accuracy and robustness of three classes of methods for solving two-phase incompressible flows on a staggered grid. Here, the unsteady two-phase flow equations are simulated by finite volumes and penalty methods using implicit and monolithic approaches (such as the augmented Lagrangian and the fully coupled methods), where all velocity components and pressure variables are solved simultaneously (as opposed to segregated methods). The interface tracking is performed with a Volume-of-Fluid (VOF) method, using the Piecewise Linear Interface Construction (PLIC) technique. The home code Fugu is used for implementing the various methods. Our target application is the simulation of two-phase flows at high density and viscosity ratios, which are known to be challenging to simulate. The resulting strategies of monolithic approaches will be proven to be considerably better suited for these two-phase cases, they also allow to use larger time step than segregated methods.

Highlights

Understanding the physics of unsteady incompressible two-phase flows at large contrast ratios [1] and their numerical modeling via Navier-Stokes equations has become an important tool that allows understanding further physics of multiphase flows and controls the behavior of these flows in several industrial and environmental applications
While the vast majority of related documented studies rely on explicit and segregated methods, we describe here a fully coupled method for dealing with velocity-pressure coupling, to take advantage of its robustness, principally for the simulation of two-phase flows at large density and viscosity ratios, which has been little studied in the literature
We have conducted different simulations of two-phase flow modeling, to demonstrate the accuracy and performance of our new fully coupled solver compared to existing resolution algorithms, and implemented in a homemade code (FUGU) developed at MSME Research Laboratory

Summary

Introduction

Understanding the physics of unsteady incompressible two-phase flows at large contrast ratios [1] and their numerical modeling via Navier-Stokes equations has become an important tool that allows understanding further physics of multiphase flows and controls the behavior of these flows in several industrial and environmental applications. They remain among the most difficult to simulate numerically for two correlated reasons: the difficulties in the mathematical formalism of these equations resulting from the velocity-pressure coupling [2] and the numerical processing of the interfaces [3] which can be decoupled from solving the Navier-Stokes system. This class of methods fall along to one of the two following approaches: Front Tracking and

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Conclusion