基于WENO格式有限體積法的鐵磁流體兩相流相場方法

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中圖分類號： 0359÷.1 文獻(xiàn)標(biāo)志碼：A 文章編號：1000-582X（2025）04-067-17

A finite volume-based phase field method for two-phase ferrofluid flows

ZHANG Shaosong'， ZHANG Liangqi'， CHENG Liming'， WANG Xiaoshuang2， XIAO Yao'， ZENG Zhong' （1.College of Aerospace Engineering，Chongqing University， Chongqing 40o044， P. R. China； 2.ShanghaiChongqing Institute of Artificial Intelligence， Chongqing 401332， P. R. China）

Abstract：This paper presents a finite volume method based on the weighted esentially non-oscillatory（WENO） scheme to develop a phase field method for simulating two-phase ferrofluid flows.The incompressible Navier

Stokes quations is used to describe fluide flow，the Cahn-Hillard equation is adopted to capture interfacial motion of two-phase flow， and the Maxwellequation is used to describe external magnetic field distribution.At the same time， adding Kelvin force and surface tension to the fluid flow control equation to achieve the description of interface dynamic behavior by magnetic field.To address the chalenges posed bythe fourth-order nonlinear diffusion terms，the Cahn-Hilliard equation is decomposed into two Helmholtz equations.The fifthorder WENO scheme is employed to handle the convection term， enhancing computational accuracy and mitigating numerical oscillations. Validation through Zalesak's disk problem shows that the proposed method achieves higher phase interface capture accuracy compared to existing references，while maintaining performance comparable to high-precision phase field methods.The method isapplied to investigate droplet shear deformation， revaling its capability to capture more satellte droplets. Moreover，research on the shear deformation of ferromagnetic fluid droplets under the influence of magnetic fields and with lower capillary numbers indicatesthat the magnetic interfacial force favors droplet deformation when the external magnetic field direction aligns with the hydrodynamic deformation.Furthermore， increasing the magnetic field intensity leads to droplet splitting. Conversely， when the magnetic field is nearly perpendicular to the deformation direction， a low-intensity field alters the deformation trajectory，while a high intensity magnetic field enforces deformation along the magnetic field direction.

Keywords： phase-field method； finite volume method； ferrofluid droplets； magnetic field control

鐵磁流體憑借其優(yōu)越的變形能力和磁場可控性而受到廣泛應(yīng)用。（剩余11908字）