应用数学2025，Vol.38Issue(3)：607-624,18.
Cahn-Hilliard-Navier-Stokes方程的一类新的高效数值格式
A New Class of Efficient Schemes for the Cahn-Hilliard-Navier-Stokes Equations
摘要
Abstract
In this paper,we construct a new class of efficient and high-order schemes for the Cahn-Hilliard-Navier-Stokes equations with periodic boundary conditions.These schemes are based on two types of scalar auxiliary variable approaches.By using a new pressure correction method,the accuracy of the pressure has been greatly improved.Furthermore,one only needs to solve a series of fully decoupled linear equations with constant coefficients at each time step.In addition,we prove the unconditional energy stability of the schemes,rigorously.Finally,plenty of numerical simulations are carried out to verify the convergence rates,stability,and effectiveness of the proposed schemes numerically.关键词
Cahn-Hilliard-Navier-Stokes方程/标量辅助变量/压力校正/无条件能量稳定Key words
Cahn-Hilliard-Navier-Stokes equation/Scalar auxiliary variable/Pressure-correction/Unconditional energy stability分类
数学引用本文复制引用
王李靖,王旦霞,张建文..Cahn-Hilliard-Navier-Stokes方程的一类新的高效数值格式[J].应用数学,2025,38(3):607-624,18.基金项目
Supported by the Research Project Supported of Shanxi Scholarship Council of China(No.2021-029),Shanxi Provincial International Cooperation Base and Platform Project(202104041101019)and Shanxi Province Natural Science Research(202203021211129) （No.2021-029）
