Three linear, unconditionally stable, second order decoupling methods for the Allen--Cahn--Navier--Stokes phase field model
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.
Cite
@article{arxiv.2108.07470,
title = {Three linear, unconditionally stable, second order decoupling methods for the Allen--Cahn--Navier--Stokes phase field model},
author = {Ruonan Cao and Nan Jiang and Huanhuan Yang},
journal= {arXiv preprint arXiv:2108.07470},
year = {2022}
}
Comments
24 pages, 7 figures, 4 tables