CAREER: Analysis and Numerics for the Dynamics of Fluids under Magnetic Forces

职业：磁力下流体动力学的分析和数值模拟

基本信息

批准号：
2042454
负责人：
Franziska Weber
金额：
$ 50万
依托单位：
Carnegie-Mellon University
依托单位国家：
美国
项目类别：
Continuing Grant
财政年份：
2021
资助国家：
美国
起止时间：
2021-07-01 至 2026-06-30
项目状态：
未结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=2042454&HistoricalAwards=false
关键词：
CAREER Analysis Numerics Dynamics Fluids

项目摘要

While invisible to the eye, magnetic fields contribute to many phenomena in nature and aspects of daily life, such as ocean tides, solar flares, or electric motors. Additionally, they are used to manipulate materials for industrial applications like precision sensors, liquid-metal cooling of nuclear reactors, or magnetic drug targeting. The goal of this project is to study several mathematical models involving fluids forced by magnetic fields, and develop numerical algorithms for their simulation on a computer. This will benefit practical applications in engineering and in physical and biomedical sciences. Educational components targeting students at the high school, undergraduate and graduate level, are integrated with the research activities. The research program includes projects suitable for graduate and undergraduate research. Curriculum development for undergraduate courses in computational mathematics, and outreach to high school students in the form of an interdisciplinary math and engineering summer camp, will be undertaken. The objective of this project is the mathematical investigation of three important problems motivated from science and engineering. The first is the numerical simulation of liquid crystals subjected to magnetic fields, which are used in LCD screens. The second deals with mathematical aspects of magnetohydrodynamics turbulence in order to gain more insight into the emergence and existence of the magnetic field of the earth. The third problem concerns the question of how experimental data affects mathematical models: Probabilistic tools will be employed to develop algorithms for uncertainty quantification in compressible flows applications. These problems are described mathematically by nonlinear systems of mixed type partial differential equations (PDEs). The mathematical treatment of these systems requires the development of new analytical techniques and innovative algorithms for their simulation. The finite difference and finite volume schemes constructed in this project will be analyzed with mathematical tools such as energy estimates, compensated compactness and relative entropy methods to prove robustness and convergence.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.

虽然眼睛看不见，但磁场在自然界和日常生活中的许多现象（例如海潮，太阳耀斑或电动机）中有助于许多现象。此外，它们用于操纵工业应用材料，例如精确传感器，核反应堆的液态冷却或磁性药物靶向。该项目的目的是研究涉及磁场强迫的流体的几种数学模型，并为其在计算机上的模拟开发数值算法。这将受益于工程以及物理和生物医学科学方面的实际应用。针对高中，本科生和研究生层面的学生的教育组成部分与研究活动融为一体。该研究计划包括适合研究生和本科研究的项目。将开展计算数学本科课程的课程开发，并以跨学科的数学和工程夏令营的形式向高中生开发。该项目的目的是对科学和工程促进的三个重要问题的数学研究。首先是经受磁场的液晶的数值模拟，该液晶在LCD屏幕中使用。第二个涉及磁流失动力学湍流的数学方面，以便对地球磁场的出现和存在更多地了解。第三个问题涉及实验数据如何影响数学模型的问题：将使用概率工具来开发可压缩流应用中不确定性定量的算法。这些问题通过混合型部分微分方程（PDE）的非线性系统来描述。这些系统的数学处理需要开发新的分析技术和创新算法以进行模拟。该项目中构建的有限差异和有限体积方案将通过数学工具（例如能量估计，补偿紧凑性和相对熵方法）进行分析，以证明稳健性和融合性。该奖项反映了NSF的法定任务，并被认为是通过基金会的智力优点和广泛影响的评估来评估的，并被认为是值得的。