CMG: Collaborative Research: Adaptive Numerical Methods for Shallow Water Circulation with Applications to Hurricane Storm Surge Modeling

该项目的目标是通过改进数学模型，开发能够在不同尺度上解析高能流特征的动态自适应数值算法，提高计算分辨率和改进沿海地区的物理描述，以及有效地利用并行计算来提高风暴潮模拟的准确性和鲁棒性。该项目本质上是跨学科的，涉及数学建模、数值分析、计算科学、海岸工程、地貌学和海洋科学等方面。研究小组将开发改进的风暴潮物理模型，包括环流、沉积物和污染物运输的耦合，以及在高分辨率计算域上定义的波浪模型。本文将制定和分析用于数值求解这些模型的自适应计算方法。这项研究的结果将包括基于这些改进的物理模型和自适应算法的高效模拟器，设计用于大规模并行计算。该模拟器将根据实验室和现场数据进行数值验证和相关基准验证。这些想法的综合将导致墨西哥湾沿岸和美国东海岸的一个完全可操作的飓风风暴潮模型，能够在风暴接近登陆时预测风暴潮并研究风暴的后果。正如最近发生的卡特里娜飓风、丽塔飓风和威尔玛飓风所表明的那样，预测和研究飓风风暴潮影响的能力是关系到国家利益的关键问题。卡特里娜飓风是美国历史上造成损失最大、死亡人数第五多的飓风；然而，如果有更好的预报、设计和准备，这场风暴造成的大部分破坏和生命损失是可以避免的。飓风风暴潮模型可用于在风暴接近登陆时预测洪水，以便进行应急管理，并可用于设计和实施改进的保护系统，包括堤防、湿地、海堤和防洪闸。风暴潮的计算机模型已经开发出来；然而，直到最近几年，计算能力和分辨率才开始以合理的确定性程度对这些事件进行建模。在这个项目中，研究人员将开发数学模型和最先进的计算算法和技术，以模拟飓风和其他热带事件引起的风暴潮。该项目将涉及数学家、海岸工程师和海洋科学家之间的合作。这项研究工作将加强对未来科学家和工程师的培训，所开发的方法将影响沿海工程和海洋科学的其他问题，包括水质、航运和港口、海洋生态、海军作战、天气和气候以及湿地退化。

The objectives of this project are to improve the accuracy and robustness of storm-surge simulation through improved mathematical modeling, the development of dynamically adaptive numerical algorithms capable of resolving energetic flow features on different scales, increased computational resolution and improved physical description of coastal regions, and through efficient use of parallel computation. The project is inherently interdisciplinary, involving aspects of mathematical modeling, numerical analysis, computational science, coastal engineering, geomorphology, and marine science. The research team will develop improved physical models of storm surges including coupling of circulation, sediment and contaminant transport, and wave models defined on highly resolved computational domains. Adaptive computational methods for solving these models numerically will be formulated and analyzed. The results of this investigation will include an efficient simulator based on these improved physical models and adaptive algorithms, designed for large-scale parallel computation. The simulator will be verified numerically and validated on relevant benchmarks based on laboratory and field data. The synthesis of these ideas will lead to a fully operational hurricane storm-surge model for the Gulf Coast and eastern seaboard of the U.S., capable of predicting storm surges as storms approach landfall and studying the aftermath of storms.As recent events such as Hurricanes Katrina, Rita, and Wilma have demonstrated, the ability to predict and study the effects of hurricane storm surges is a problem of critical national interest. Hurricane Katrina alone is the costliest and fifth-deadliest hurricane in U.S. history; yet with better forecasting, design, and preparation, much of the devastation and loss of life caused by this storm could have been avoided. Hurricane storm-surge models can be used to predict flooding as storms approach landfall for the purposes of emergency management, and can be used in the design and implementation of improved protection systems, including levees, wetlands, seawalls, and flood gates. Computer models of storm surges have been developed; however, only within the past few years has the computational power and resolution been available to begin to model these events with any reasonable degree of certainty. In this project, the investigators will develop mathematical models and state-of-the-art computational algorithms and technologies for simulating storm surges due to hurricanes and other tropical events. The project will involve collaboration among mathematicians, coastal engineers, and marine scientists. The research effort will enhance the training of future scientists and engineers, and the developed methodology will impact other problems in coastal engineering and marine science, including water quality, shipping and ports, marine ecology, naval operations, weather and climate, and wetland degradation.