On fully decoupled MSAV schemes for the Cahn-Hilliard-Navier-Stokes model of Two-Phase Incompressible Flows

TL;DR

This paper develops fully decoupled, energy-stable time discretization schemes for the coupled Cahn-Hilliard-Navier-Stokes system using MSAV and pressure-correction methods, with proven optimal error convergence.

Contribution

It introduces linear, fully decoupled, unconditionally energy-stable schemes for the two-phase flow model, with rigorous error analysis and numerical validation.

Findings

Schemes are linear, fully decoupled, and unconditionally energy stable.

Error analysis confirms optimal convergence rates.

Numerical experiments verify theoretical results.

Abstract

We construct first- and second-order time discretization schemes for the Cahn-Hilliard-Navier-Stokes system based on the multiple scalar auxiliary variables approach (MSAV) approach for gradient systems and (rotational) pressure-correction for Navier-Stokes equations. These schemes are linear, fully decoupled, unconditionally energy stable, and only require solving a sequence of elliptic equations with constant coefficients at each time step. We carry out a rigorous error analysis for the first-order scheme, establishing optimal convergence rate for all relevant functions in different norms. We also provide numerical experiments to verify our theoretical results.