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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

基本信息

批准号：
1818783
负责人：
XIAOFENG YANG
金额：
$ 5.72万
依托单位：
University of South Carolina at Columbia
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=1818783&HistoricalAwards=false
关键词：
Collaborative Research Models Algorithms Simulations

项目摘要

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.

两相铁磁流体流动受外加磁场的控制，在各个科学和工程领域得到了广泛的应用。两相铁磁流体混合物的流动通常包括流体动力学、界面运动、本征粒子自旋、磁化场和感应磁场的耦合。期望本文的研究不仅能为两相铁磁流体系统建立可靠的适定性模型和有效的数值算法，而且可以通过数值模拟将数学模型、分析和编码的适用范围扩展到各种当前感兴趣的物理问题。所提出的研究将产生高效、最佳收敛、易于实现、能量稳定的数值算法，以及公开可用的有限元程序。它将为本科生和研究生提供充分和宝贵的机会，在数学建模、计算数学和机械工程领域接受多学科培训，并为科学和工程应用开发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、方法和软件包传播给更多的工程师和科学家，以解决他们的实际问题，在专业会议和学术讨论会上展示研究成果，并在国内/国际会议上组织相关工作的专题会议/小型研讨会。该项目的智力优势在于为耦合自由界面、流体动力学、磁场、感应磁场和本征粒子自旋的高度非线性两相磁流体系统开发合适的数学模型和设计高效而精确的方案。由于两相铁磁流体系统之间复杂的非线性耦合作用，对其建模和数值模拟所带来的挑战几乎没有得到解决。所提出的模型在热力学上是一致的，因此保持了能量耗散定律。利用有限元方法处理复杂边界的优点，所提出的格式具有高效、准确、易于实现和能量稳定的特点，并采用了一些离散的能量耗散定律，其优点是允许大的时间步长和可控的误差界来准确地捕捉界面奇异性。此外，这些模型、数值算法和模拟将有助于更好地理解各种具有实际意义的物理问题，例如基于铁流体的新材料。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。