Multi-Scale Computational Methods for Coastal Flooding

该国海岸线上的洪水可能会给生命和财产带来毁灭性的后果，就像飓风卡特里娜和桑迪所看到的那样。努力保护我们的海岸线不受这些事件中最危险的事件的影响，对我们国家海岸线的可持续未来至关重要。该项目的目标是提供一种手段，提高我们预测和预测这些事件的能力，同时考虑到旨在保护高危人群的关键沿海基础设施。然而，这项工作不仅能够通过更好的预测来直接减少生命损失和经济影响，而且还能够应用数学和计算来开始提出和回答关键问题，例如，我想要建造一道海堤，我应该把它放在哪里，它应该有多高？这些问题的背景也是至关重要的，预算限制和最佳保护当然是这一努力的核心，该项目旨在使人们能够回答这些问题。该项目开发了能够回答与应对海啸和风暴潮造成的沿海洪灾的气候变化适应战略有关的问题的数值方法。这两种类型的事件在过去都证明了自己具有巨大的破坏性，并有望在未来如此。不幸的是，随着气候变化，这些事件可能会变得更糟，无论是由于海平面上升还是由于危险风暴可能性的变化，我们解决沿海洪水的威胁对世界海岸线的可持续生存至关重要。拟议的工作重点是开发数值方法，其中包括亚网格规模的结构，以帮助保护具有海堤等屏障的沿海社区。这项工作的基础将是GeoClaw框架，这是一种有限体积、波浪传播和结构化网格代码，此前已在海啸和风暴潮事件中得到验证。GeoClaw通过使用自适应网格细化(AMR)和本地时间步长来解决沿海洪水问题的一些多尺度性质，但由于所需的解决方案，在没有重大惩罚的情况下努力解决精细结构。拟议的工作侧重于表示次网格级别的障碍，而不需要完全解决这些结构。这将通过开发一种新的黎曼解算器来实现，该解算器将能够表示网格单元边缘的零宽度障碍。然后，这种能力将与h盒和半拉格朗日方法结合使用，从而允许屏障在相对于网格的放置方面具有灵活的参数化。然后，该方法将在实际案例中进行测试，并被纳入一个更大的优化框架，该框架旨在寻找最优的适应解决方案，强调灵活规范的屏障的能力。

Flooding along the nation's coastlines can lead to devastating consequences both to life and property as seen in Hurricanes Katrina and Sandy. Efforts to protect our coastlines from the most dangerous of these events is critical to our sustainable future along our nation's coastlines. The goal of this project is to provide a means for improving our ability to forecast and predict these events while taking into account key coastal infrastructure that are designed to protect at-risk populations. This work not only enables direct reduction of loss of life and economic impact via better forecasts however, it also enables the application of mathematics and computation that can start to ask and answer critical questions such as "I want to build a sea-wall, where should I put it and how high should it be?". The context of these questions is also critical, budgetary constraints and optimal protection are of course central to this effort and this projects aims to enable answering these questions as well.The project develops numerical methods that can answer questions related to climate change adaptation strategies addressing coastal flooding due to tsunamis and storm surge. Both types of events have in the past proven themselves to be immensely destructive and promise to be so in the future. Unfortunately with climate change these events could be made worse, whether due to rising sea-levels or changes to the likelihood of dangerous storms, it is critical to a sustainable existence along the coastlines of the world that we address the threat of coastal flooding. The work proposed focuses on developing numerical methods that include sub-grid-scale structures that help protect coastal communities with barriers such as sea-walls. The basis of the work will be the GeoClaw framework, a finite-volume, wave- propagation, and structured- grid code that has previously been validated for both tsunami and storm surge events. GeoClaw addresses some of the multi-scale nature of the coastal flooding problem by using adaptive mesh refinement (AMR) and local time stepping but struggles to resolve fine-scale structures without significant penalty due to the resolutions required. The work proposed focuses on representing barriers at the sub-grid-scale level without the need for fully resolving these structures. This will be accomplished by the development of a new Riemann solver that will be able to represent zero-width barriers at grid cell edges. This capability will then be used in conjunction with h-box and semi-Lagrangian methods allowing the barriers to have flexible parameterizations in terms of placement with respect to the grid. The method will then be tested on realistic cases and be incorporated into a larger optimization framework that is geared towards finding optimal adaptation solutions emphasizing the capabilities of the flexible specification of the barrier.