A Rotational Pressure-Correction Scheme for Incompressible Two-Phase Flows with Open Boundaries

TL;DR

This paper introduces a new rotational pressure-correction scheme and open boundary conditions for simulating two-phase flows with open boundaries, ensuring stability and physical accuracy in complex scenarios.

Contribution

It presents a novel algorithm that simplifies the linear systems for two-phase outflow simulations with open boundaries, maintaining stability and accuracy despite variable densities and viscosities.

Findings

The method produces physically accurate results compared to theory and experiments.

It demonstrates long-term stability in simulations with large density and viscosity contrasts.

The algorithm results in constant coefficient matrices, simplifying computations.

Abstract

Two-phase outflows refer to situations where the interface formed between two immiscible incompressible fluids passes through open portions of the domain boundary. We present in this paper several new forms of open boundary conditions for two-phase outflow simulations within the phase field framework. In addition, we also present a rotational pressure-correction based algorithm for numerically treating these open boundary conditions. Our algorithm gives rise to linear algebraic systems for the velocity and the pressure that involve only constant and time-independent coefficient matrices after discretization, despite the variable density and variable viscosity of the two-phase mixture. By comparing simulation results with the theory and the experimental data, we show that the method developed herein produces physically accurate results. We also present numerical experiments to demonstrate the long-term stability of the method in situations where large density contrast, large viscosity contrast, and backflows are present at the two-phase outflow/open boundaries.