Three linear, unconditionally stable, second order decoupling methods for the Allen--Cahn--Navier--Stokes phase field model

TL;DR

This paper introduces three novel, unconditionally stable, second-order decoupling numerical methods for the complex Allen--Cahn--Navier--Stokes phase field model, enhancing stability and efficiency in simulating two-phase flows.

Contribution

The paper presents three new linear, unconditionally stable, second-order decoupling algorithms based on Crank--Nicolson leap-frog discretization for the ACNS model, with proven long-term stability.

Findings

Algorithms are unconditionally stable over long time periods.

Numerical examples confirm convergence rate and efficiency.

Methods effectively decouple complex phase field equations.

Abstract

Hydrodynamics coupled phase field models have intricate difficulties to solve numerically as they feature high nonlinearity and great complexity in coupling. In this paper, we propose three second order, linear, unconditionally stable decoupling methods based on the Crank--Nicolson leap-frog time discretization for solving the Allen--Cahn--Navier--Stokes (ACNS) phase field model of two-phase incompressible flows. The ACNS system is decoupled via the artificial compression method and a splitting approach by introducing an exponential scalar auxiliary variable.We prove all three algorithms are unconditionally long time stable. Numerical examples are provided to verify the convergence rate, unconditional stability, and computational efficiency.