针对卡恩-希利亚德-达西系统的完全解耦无条件稳定的克兰-尼科尔森跃迁数值方法

IF 2.1 3区 数学 Q1 MATHEMATICS, APPLIED Numerical Methods for Partial Differential Equations Pub Date : 2024-01-30 DOI:10.1002/num.23087
Yali Gao, Daozhi Han
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引用次数: 0

摘要

我们开发了两种完全解耦的线性二阶精确数值方法,这些方法无条件能量稳定,可用于求解多孔介质或 Hele-Shaw 单元中两相流动的 Cahn-Hilliard-Darcy 方程。在对 Cahn-Hiliard 方程进行离散化时,采用了隐式-显式 Crank-Nicolson 跃迁法,以获得线性方案。此外,还分别采用了人工压缩技术和压力校正方法,从而可以独立求解卡恩-希利亚德方程和达西压力更新。我们确定了这些方案的无条件长期稳定性。为了证明数值方法的准确性和稳健性,我们进行了大量的数值实验,包括对雷利-泰勒不稳定性、萨夫曼-泰勒不稳定性(指状现象)的模拟。
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Fully decoupled unconditionally stable Crank–Nicolson leapfrog numerical methods for the Cahn–Hilliard–Darcy system
We develop two totally decoupled, linear and second-order accurate numerical methods that are unconditionally energy stable for solving the Cahn–Hilliard–Darcy equations for two phase flows in porous media or in a Hele-Shaw cell. The implicit-explicit Crank–Nicolson leapfrog method is employed for the discretization of the Cahn–Hiliard equation to obtain linear schemes. Furthermore the artificial compression technique and pressure correction methods are utilized, respectively, so that the Cahn–Hiliard equation and the update of the Darcy pressure can be solved independently. We establish unconditionally long time stability of the schemes. Ample numerical experiments are performed to demonstrate the accuracy and robustness of the numerical methods, including simulations of the Rayleigh–Taylor instability, the Saffman–Taylor instability (fingering phenomenon).
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来源期刊
CiteScore
7.20
自引率
2.60%
发文量
81
审稿时长
9 months
期刊介绍: An international journal that aims to cover research into the development and analysis of new methods for the numerical solution of partial differential equations, it is intended that it be readily readable by and directed to a broad spectrum of researchers into numerical methods for partial differential equations throughout science and engineering. The numerical methods and techniques themselves are emphasized rather than the specific applications. The Journal seeks to be interdisciplinary, while retaining the common thread of applied numerical analysis.
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