Coupling Complex Flow and Transport Phenomena

拟议项目的目标是准确地模拟地下水污染和败血症模型中出现的复杂流动和输送现象。地下水占世界淡水的三分之二。这种对人类活动至关重要的资源不断受到污染的威胁。当人为的、有时是自然发生的物质溶解在补给地下水的水中时，地下水就会受到污染。通常，由于地下水与湖泊和河流相连，这些地表水的污染意味着对含水层的污染。因此，了解河流、湖泊和含水层耦合系统的流动和运输是很重要的。在第一个应用中，研究了这种复杂的多物理耦合。在本工作中建模的第二个应用涉及败血症，在美国，败血症是危重患者死亡的主要原因。脓毒症可以定义为细菌感染引起的一种不受控制的炎症反应。到今天为止，患者可以选择的治疗方法很少。模拟伴随脓毒症的炎症和器官功能障碍可以帮助理解这个复杂的问题。建模过程包括确定关键化学成分及其在不同子域中的相互作用，如器官、上皮层和血液动脉。描述这两种应用的基本数学方程是相似的。这些方程是从连续介质力学的平衡方程推导出来的，这些平衡方程表示在流体中运动的任意体积的质量、动量和能量的守恒定律。作为该项目的一部分，将开发高效和可靠的数值方法。一个项目的成果将是一种对环境工程师和医务人员都有利的计算工具。一方面，可以模拟出清理受污染地下水的有效策略。同时，更好地了解细菌感染引起的炎症反应将有助于设计脓毒症的治疗方案。这个项目的另一个影响将是刺激参与研究项目的本科生和研究生的发现过程。拟议项目的教育活动包括开发一个新的建模课程，设立计算和应用数学硕士学位，为研究生和本科生提供持续的指导和他们参与国际合作的机会，以及增加包括少数族裔在内的获得数学硕士或博士学位的学生数量。

The objective of the proposed project is to accurately model complex flow and transport phenomena arising in groundwater contamination and in sepsis modeling.Groundwater forms two-thirds of the world's fresh water. This resource, vital to human activities, is constantly threatened by contamination. Groundwater becomes contaminated when man-made and sometimes naturally-occurring substances are dissolved in waters recharging the groundwater. Often, as groundwater is connected with lakes and rivers, the pollution of these surface waters implies the pollution of aquifers. Thus, it is important to understand the flow and transport of the coupled system of rivers, lakes, and aquifers. In this first application, such complex multiphysics couplings are studied.The second application modeled in this work involves sepsis, which in the U.S. is the primary cause of death in critically ill patients. Sepsis can be defined as an uncontrolled inflammatory response due to bacterial infection. As of today, there are very few therapeutic options available to patients. Simulating inflammation and organ dysfunction that accompany sepsis can help understand this complex problem. The modeling process consists of identifying key chemical components and their interaction in different subdomains such as organs, epithelial layers, and blood arteries.The underlying mathematical equations characterizing both applications are similar. Those equations are derived from the balance equations of continuum mechanics that express the conservation laws for mass, momentum, and energy of an arbitrary volume moving within a fluid. Efficient and reliable numerical methods will be developed as a part of this project. One project output will be a computational tool that is beneficial to both environmental engineers and medical personnel. On one hand, effective strategies for clean-up of contaminated groundwaters can be simulated. At the same time,a better understanding of the inflammatory response due to bacterial infection will lead to the design of therapeutic solutions for sepsis. Another impact of this project will be the stimulation of the discovery process for undergraduate and graduate students involved in the research project.Educational activities for the proposed project include the development of a new modeling course, the creation of a Master's degree in Computational and Applied Mathematics, the continuous mentorship of graduate and undergraduate students and their exposure to international collaborations, and an increase in the number of students, including minorities, graduating with a Master or Ph.D. degree in Mathematics.