Ruonan Cao | Searcharxiv

arXiv2025

A linear, unconditionally stable, second order decoupled method for the Ericksen-Leslie model with SAV approach

In this paper, we present a second order, linear, fully decoupled, and unconditionally energy stable scheme for solving the Erickson-Leslie model. This approach integrates the pressure correction method with a scalar auxiliary variable technique. We rigorously demonstrate the unconditional energy stability of the proposed scheme. Furthermore, we present several numerical experiments to validate its convergence order, stability, and computational efficiency.

math.AP↗

arXiv2022

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

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.

math.NA↗