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

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.

Numerical Study of Compressible and Weak Compressible Flows in Channel Based on Artificial Compressibility Method and Fully Artificial Compressibility Method

“…For instance, with C 2 =100 we need around 3100 time-step to get the pressure convergence compared to 12100 time-step for FAC-method; almost (74%) rising. Also, this comparison is very clear for C 2 =100, where the level of time increments to reach convergence with for FAC-method is five times more than with AC-method (1100 time-step for AC-method and 5000 time-step for FAC-method), what is found is match with [8,14,15,16].…”

“…The level of convergence for the velocity component is high compared to pressure because of the influence of nonlinearity behavior. Thus, we can conclude that the use of AC-method is much easier than FAC-method or direct method [8,14,15,16]. More details are presented in Table1.…”

A Compressible Formulation of the One-Fluid Model for Two-Phase Flows

“…The original formulation was introduced by [7] and recently extended to all-Mach flows by [8] to account for heat diffusion between two different compressible phases. In the present work, we extend this formulation by maintaining a strong coupling between velocity and pressure variables through the use of a monolithic solver [9][10][11] and by preserving the consistency between mass transport and momentum via a momentum conserving scheme [12].…”

Numerical Simulation of Multiphase Multicomponent Flow in Porous Media: Efficiency Analysis of Newton-Based Method

“…in order to simulate multiphase, multicomponent flow in porous media. Other methods and schemes can be found in [9][10][11][12]. We could find Newton's method often in current research works in this area.…”