A Novel Energy Stable Numerical Scheme for Navier-Stokes-Cahn-Hilliard Two-phase Flow Model with Variable Densities and Viscosities

TL;DR

This paper introduces a new, fully decoupled, linear, and unconditionally energy stable numerical scheme for simulating two-phase flows with variable densities and viscosities, ensuring accuracy and robustness.

Contribution

The paper presents a novel numerical scheme that is decoupled, linear, and energy stable for two-phase flow models with variable properties, incorporating an intermediate velocity approach.

Findings

Scheme maintains discrete energy law.

Numerical results validate accuracy and robustness.

Scheme is fully decoupled and linear.

Abstract

A novel numerical scheme including time and spatial discretization is offered for coupled Cahn-Hilliard and Navier-Stokes governing equation sys-tem in this paper. Variable densities and viscosities are considered in the nu-merical scheme. By introducing an intermediate velocity in both Cahn-Hilliard equation and momentum equation, the scheme can keep discrete energy law. A decouple approach based on pressure stabilization is implemented to solve the Navier-Stokes part, while the stabilization or convex splitting method is adopt-ed for the Cahn-Hilliard part. This novel scheme is totally decoupled, linear, unconditionally energy stable for incompressible two-phase flow diffuse inter-face model. Numerical results demonstrate the validation, accuracy, robustness and discrete energy law of the proposed scheme in this paper.