Collaborative Research: Models, Algorithms, and Simulations for Two-Phase Ferrofluid Flows in Contact with a Solid Surface

合作研究：与固体表面接触的两相铁磁流体流动的模型、算法和模拟

• 批准号: 1818642
• 负责人: Xiaoming He
• 金额: $ 16万
• 依托单位: Missouri University of Science and Technology
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2018
• 资助国家: 美国
• 起止时间: 2018-08-01 至 2022-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1818642&HistoricalAwards=false
• 关键词: Collaborative; Research; Models; Algorithms; Simulations

Being controllable by applied magnetic fields, two-phase ferrofluid flows have found diverse applications in various science and engineering fields. Flows of two-phase ferrofluid mixtures usually involve the coupling of hydrodynamics, interface motion, intrinsic particle spins, magnetization field, and induced magnetic field. It is expected that the proposed research will not only lead to reliable well-posed models, efficient numerical algorithms for the two-phase ferrofluid system, but also extend the applicability of mathematical models, analyses and codes to various physical problems of current interest through numerical simulations. The proposed research will produce efficient, optimally convergent, easily implemented, energy stable numerical algorithms, as well as publicly available finite element codes. It will provide ample and valuable opportunities for undergraduate and graduate students to receive multidisciplinary training in the areas of mathematical modeling, computational mathematics, and mechanical engineering, and to develop state-of-the-art mathematical models and numerical algorithms for science and engineering applications. Starting from this collaborative work, the investigators plan to disseminate the developed models, methods and software packages to more engineers and scientists for solving their realistic problems, present the research in professional conferences and colloquia, and organize special sessions/minisymposiums in domestic/international conferences for related works.The intellectual merit of this project lies in the challenge to develop suitable mathematical models and design efficient and accurate schemes for the highly nonlinear two-phase ferrofluid system, which couples free interfaces, hydrodynamics, magnetization field, induced magnetic field, and intrinsic particle spins. Very few efforts have been made to address the induced modeling/numerical challenges of the two-phase ferrofluid system due to the complicated nonlinear couplings among these constituents. The proposed models are thermodynamically consistent and thus preserve the energy dissipation laws. With strengths of the finite element methods in dealing with the complex boundary, the proposed numerical schemes are efficient, accurate, easily implemented, and energy stable with some discrete energy dissipation laws which have advantages of allowing the large time step and controlled error bound to capture the interfacial singularities accurately. In addition, the models, numerical algorithms and simulations will contribute to better understandings of various physical problems of practical interests, such as new materials based on ferro fluids.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

两相纤维流体流可以通过应用磁场控制，在各种科学和工程领域中发现了各种应用。两相铁氟烯混合物的流量通常涉及流体动力学，界面运动，内在粒子旋转，磁化场和诱导磁场的耦合。预计拟议的研究不仅将导致可靠的模型，有效的两相铁体系统的有效数值算法，而且还将数学模型和代码的适用性扩展到了通过数值模拟的当前兴趣的各种物理问题的适用性。 拟议的研究将产生有效的，最佳的收敛性，易于实现的，能量稳定的数值算法以及公开可用的有限元代码。它将为本科和研究生提供足够的宝贵机会，以在数学建模，计算数学和机械工程领域接受多学科培训，并开发用于科学和工程应用程序的最先进的数学模型和数值算法。从这项合作工作开始，研究人员计划将开发的模型，方法和软件包分散给更多的工程师和科学家，以解决其现实问题，在专业会议和官方中介绍研究，并在国内/国际上组织特殊的会议/小型会议，以实现此项目的智力和精确的挑战。两相铁体系统，伴随自由接口，流体动力学，磁化场，磁场和固有的粒子自旋。由于这些成分之间复杂的非线性耦合，因此很少有努力解决两相铁体系统的诱导建模/数值挑战。所提出的模型在热力学上是一致的，因此可以保留耗能法则。有限元方法在处理复杂边界方面的优势，提出的数值方案具有有效，准确，易于实现和稳定的能量，并具有一些离散的能量耗散法，这些法律具有允许较大的时间步长和可控制的误差，以准确捕获界面的误差。此外，模型，数值算法和仿真将有助于更好地理解实际利益的各种物理问题，例如基于Ferro流体的新材料。这项奖项反映了NSF的法定任务，并被认为是通过基金会的知识分子优点和更广泛的审查标准来评估值得通过评估来支持的。

项目成果

A diffuse interface model and semi-implicit energy stable finite element method for two-phase magnetohydrodynamic flows

两相磁流体动力流的扩散界面模型和半隐式能量稳定有限元方法

• DOI: 10.1016/j.cma.2019.07.022
• 发表时间: 2019-11
• 期刊: Computer Methods in Applied Mechanics and Engineering
• 影响因子: 7.2
• 作者: Yang Jinjin;Mao Shipeng;He Xiaoming;Yang Xiaofeng;He Yinnian
• 通讯作者: He Yinnian

Unconditionally stable numerical methods for Cahn-Hilliard-Navier-Stokes-Darcy system with different densities and viscosities

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
• 发表时间: 2022-01
• 期刊: Journal of Computational Physics
• 影响因子: 4.1
• 作者: Yali Gao;Daozhi Han;Xiaoming He;Ulrich Rüde
• 通讯作者: Ulrich Rüde

Decoupled, Linear, and Unconditionally Energy Stable Fully Discrete Finite Element Numerical Scheme for a Two-Phase Ferrohydrodynamics Model

• DOI: 10.1137/19m1288280
• 发表时间: 2021
• 期刊: SIAM J. Sci. Comput.
• 作者: Guodong Zhang;Xiaoming He;Xiaofeng Yang

Deformation and coalescence of ferrodroplets in Rosensweig model using the phase field and modified level set approaches under uniform magnetic fields

• DOI: 10.1016/j.cnsns.2020.105213
• 发表时间: 2020-06
• 期刊: Commun. Nonlinear Sci. Numer. Simul.
• 作者: Feng Bai;Daozhi Han;Xiaoming He;Xiaofeng Yang

A fully-discrete decoupled finite element method for the conserved Allen–Cahn type phase-field model of three-phase fluid flow system

• DOI: 10.1016/j.cma.2021.114376
• 发表时间: 2022-02
• 期刊: Computer Methods in Applied Mechanics and Engineering
• 影响因子: 7.2
• 作者: Xiaofeng Yang;Xiaoming He