Unconditionally stable numerical methods for Cahn-Hilliard-Navier-Stokes-Darcy system with different densities and viscosities
Unconditionally stable numerical methods for Cahn-Hilliard-Navier-Stokes-Darcy system with different densities and viscosities
复制标题
不同密度和粘度Cahn-Hilliard-Navier-Stokes-Darcy系统的无条件稳定数值方法
DOI：
10.1016/j.jcp.2022.110968
复制
发表时间：
2022-01
影响因子：
4.1
通讯作者：
Ulrich Rüde
中科院分区：
文献类型：
--
作者：
Yali Gao;Daozhi Han;Xiaoming He;Ulrich Rüde
本文采用相场方法对不同密度和粘度的两相自由渗流和两相多孔介质渗流进行了数值模拟和模拟。该模型由自由流区的Cahn-Hilliard-Navier-Stokes方程和多孔介质中的Cahn-Hilliard-Darcy方程组成，由多个区域界面条件耦合而成。结果表明，该耦合模型满足能量定律。然后，我们首先提出了一种求解该模型的耦合无条件稳定有限元方法，并分析了该方法的能量稳定性。此外，基于压力稳定和人工可压缩的思想，我们提出了一种无条件稳定的时间步长方法，它将相场变量、自由流动的速度和压力、多孔介质的速度和压力的计算解耦，从而大大降低了计算量。严格建立了有限元空间离散解耦格式的能量稳定性。我们用数值方法证明了我们的格式是收敛的和能量守恒的。文中还进行了数值实验，以说明在自由流动和多孔介质耦合条件下的两相流动特性。
In this article we consider the numerical modeling and simulation via the phase field approach for coupled two-phase free flow and two-phase porous media flow of different densities and viscosities. The model consists of the Cahn-Hilliard-Navier-Stokes equations in the free flow region and the Cahn-Hilliard-Darcy equations in porous media that are coupled by several domain interface conditions. It is showed that the coupled model satisfies an energy law. Then we first propose a coupled unconditionally stable finite element method for solving this model and analyze the energy stability for this method. Furthermore, based on the ideas of pressure stabilization and artificial compressibility, we propose an unconditionally stable time stepping method that decouples the computation of the phase field variable, the velocity and pressure of free flow, the velocity and pressure of porous media, hence significantly reduces the computational cost. The energy stability of this decoupled scheme with the finite element spatial discretization is rigorously established. We verify numerically that our schemes are convergent and energy-law preserving. Numerical experiments are also performed to illustrate the features of two-phase flows in the coupled free flow and porous media setting.
登录
查看更多内容
影响因子：
1.7
作者：
M. Hadji;A. Assala;F. Z. Nouri
通讯作者：
M. Hadji;A. Assala;F. Z. Nouri
耦合 Navier-Stokes-Cahn-Hilliard 相场模型的不连续有限体积元法
影响因子：
1.7
作者：
Li Rui;Gao Yali;Chen Jie;Zhang Li;He Xiaoming;Chen Zhangxin
通讯作者：
Chen Zhangxin
影响因子：
1.1
作者：
Jie Shen;Xiaofeng Yang
通讯作者：
Jie Shen;Xiaofeng Yang
DOI：
10.1016/j.jcp.2014.02.043
发表时间：
2014-07
期刊：
J. Comput. Phys.
影响因子：
--
作者：
Jie Chen;Shuyu Sun;Xiaoping Wang
通讯作者：
Jie Chen;Shuyu Sun;Xiaoping Wang
DOI：
--
发表时间：
2007
期刊：
--
影响因子：
--
作者：
V. Ervin;E. Jenkins;S. Sun
通讯作者：
V. Ervin;E. Jenkins;S. Sun