两相多孔介质铁磁流体模型的一个高效算法  

An Efficient Algorithm for Ferromagnetic Fluid Model of Two-Phase Porous Media

作　　者：姜莹莹 周帅 张国栋 JIANG Yingying;ZHOU Shuai;ZHANG Guodong(School of Mathematics and Information Sciences,Yantai University,Yantai 264005,China)

机构地区：[1]烟台大学数学与信息科学学院,山东烟台264005

出　　处：《烟台大学学报(自然科学与工程版)》2025年第2期143-155,共13页Journal of Yantai University(Natural Science and Engineering Edition)

基　　金：国家自然科学基金资助项目(12171415,12271468)。

摘　　要：建立了一种基于Cahn-Hilliard相场方程的两相多孔介质铁磁流体数学模型,同时建立了其能量定律。为了高效求解非线性、耦合、鞍点结构的多孔介质铁磁流体系统,应用辅助标量法(SAV方法)和零能量法(ZEC方法)的统一框架,提出了线性、时间一阶精度、完全解耦、质量守恒和无条件能量稳定的格式。进一步证明了格式的质量守恒、无条件能量稳定性和适定性。最后,通过几组数值算例验证了建立的数学模型及格式的有效性、收敛性和稳定性。A mathematical model for two-phase porous media ferromagnetic fluid based on the Cahn-Hilliard phase field equation was developed,along with its energy law.To efficiently solve the nonlinear,coupled,saddle-point structured systems in porous media ferromagnetic fluids,a unified framework combing the scalar auxiliary variable(SAV)method and the zero energy(ZEC)method was applied.This framework proposes a linear,first-order time-accurate,fully decoupled sheme that ensures mass conservation and unconditional energy stability.This approach further confirms the scheme’s mass conservation,unconditional energy stability,and suitability.Finally,the effectiveness,convergence,and stability of the mathematical model and scheme were verified through several numerical examples.

关 键 词：两相多孔介质铁磁流体 SAV-ZEC统一框架 解耦格式 无条件稳定 

分 类 号：O242.21[理学—计算数学]