Collaborative Research: Multidimensional Couplings for Flow and Transport in Porous Media

合作研究：多孔介质中流动和传输的多维耦合

• 批准号: 2111459
• 负责人: Beatrice Riviere
• 金额: $ 29.13万
• 依托单位: William Marsh Rice University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2021
• 资助国家: 美国
• 起止时间: 2021-09-01 至 2024-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2111459&HistoricalAwards=false
• 关键词: Collaborative; Research; Multidimensional; Couplings; Flow

The project focuses on the study of physical phenomena coupling different spatial scales. The mathematical and numerical analysis of these coupled problems is challenging because of the lack of smoothness in the solution. Applications of these coupled problems are many; for instance the mathematical modeling of blood flow in organs is important in understanding the mechanisms of organ perfusion, embolization and drug delivery. The project will train graduate students and undergraduate students in computational and applied mathematics. Research outcomes will be published in research journals, online and presented at scientific meetings.The overall goal of the project is the formulation, analysis and application of discontinuous Galerkin methods for the solution of coupled one-dimensional and three-dimensional flow and transport processes in porous media. The numerical analysis is challenging because weak solutions exhibit a singularity on the line source. The research team will develop and analyze numerical methods for model problems with singular data. The methods will combine novel efficient time-stepping algorithms with discontinuous finite element methods. The investigators will apply the algorithms to multidimensional couplings in organ and vasculature. The development and validation of physics-based computational models will be guided by imaging of flow and transport. Neural network based image image segmentation extracts the geometry of the organ and blood vessels. Students will be involved in the research and they will be trained in numerical analysis and scientific computing. Outreach activities will engage high school students with recent developments in computational mathematics.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.

该项目的重点是研究不同空间尺度之间相互耦合的物理现象。这些耦合问题的数学和数值分析是具有挑战性的，因为缺乏光滑的解决方案。这些耦合问题的应用有很多;例如，器官中血流的数学建模对于理解器官灌注、栓塞和药物输送的机制很重要。该项目将培训研究生和本科生在计算和应用数学。研究成果将在研究期刊、网上发表，并在科学会议上介绍。该项目的总体目标是制定、分析和应用不连续Galerkin方法，以解决多孔介质中耦合的一维和三维流动和输运过程。数值分析是具有挑战性的，因为弱解表现出奇异性的线源。研究团队将开发和分析奇异数据模型问题的数值方法。该方法将联合收割机新的有效的时间步进算法与间断有限元方法相结合。研究人员将把这些算法应用于器官和脉管系统的多维耦合。流动和运输的成像将指导基于物理学的计算模型的开发和验证。基于神经网络的图像分割提取器官和血管的几何形状。学生将参与研究，他们将接受数值分析和科学计算方面的培训。该奖项反映了NSF的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。

项目成果

PocketNet: A Smaller Neural Network for 3D Medical Image Segmentation

• 发表时间: 2021
• 期刊: ArXiv
• 作者: A. Celaya;Jonas A. Actor;Rajarajeswari Muthusivarajan;Evan Gates;C. Chung;D. Schellingerhout;B. Rivière;David T. Fuentes

Discontinuous Galerkin approximations to elliptic and parabolic problems with a Dirac line source

狄拉克线源椭圆和抛物线问题的不连续伽辽金逼近

• DOI: 10.1051/m2an/2022095
• 发表时间: 2023
• 期刊: ESAIM: Mathematical Modelling and Numerical Analysis
• 作者: Masri, Rami;Shen, Boqian;Riviere, Beatrice
• 通讯作者: Riviere, Beatrice