Time integration for diffuse interface models for two-phase flow

TL;DR

This paper introduces a new time integration scheme and stabilization techniques for diffuse interface models in two-phase flow, enabling larger time steps and improved computational efficiency over existing methods.

Contribution

It presents a novel fully implicit coupling method and stabilization techniques that significantly enhance the stability and efficiency of diffuse interface simulations.

Findings

Fully implicit scheme is stable for arbitrarily large time steps.

Stabilization techniques lift the time step restriction in explicit coupling.

The proposed methods can outperform sharp interface models in computational speed.

Abstract

We propose a variant of the $\theta$-scheme for diffuse interface models for two-phase flow, together with three new linearization techniques for the surface tension. These involve either additional stabilizing force terms, or a fully implicit coupling of the Navier-Stokes and Cahn-Hilliard equation. In the common case that the equations for interface and flow are coupled explicitly, we find a time step restriction which is very different to other two-phase flow models and in particular is independent of the grid size. We also show that the proposed stabilization techniques can lift this time step restriction. Even more pronounced is the performance of the proposed fully implicit scheme which is stable for arbitrarily large time steps. We demonstrate in a Taylor flow application that this superior coupling between flow and interface equation can render diffuse interface models even computationally cheaper and faster than sharp interface models.