Multi-Scale Computational Methods for Coastal Flooding

沿着国家海岸线的洪水会给生命和财产带来毁灭性的后果，正如卡特里娜飓风和桑迪飓风所示。努力保护我们的海岸线免受这些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，以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。这项工作不仅能够通过更好的预测直接减少生命损失和经济影响，而且还使数学和计算的应用能够开始提出和回答关键问题，如“我想建一个海堤，我应该把它建在哪里，它应该有多高？”这些问题的背景也很关键，预算限制和最佳保护当然是这项工作的核心，该项目旨在回答这些问题。该项目开发的数值方法可以回答与应对海啸和风暴潮引起的沿海洪水的气候变化适应战略相关的问题。这两种类型的事件在过去都证明了它们具有巨大的破坏性，并且在未来也会如此。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。提出的工作重点是开发包括亚电网规模结构的数值方法，这些结构有助于用海堤等屏障保护沿海社区。这项工作的基础将是GeoClaw框架，这是一个有限体积、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）和本地时间步进解决了沿海洪水问题的一些多尺度性质，但由于所需的分辨率，它很难在不造成重大损失的情况下解决精细尺度结构。提出的工作重点是在子电网尺度上表示障碍，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。这种能力将与h-box和半拉格朗日方法结合使用，允许屏障在相对于网格的位置方面具有灵活的参数化。然后，将在实际案例中对该方法进行测试，并将其纳入一个更大的优化框架，该框架旨在寻找最优适应解决方案，强调屏障灵活规格的能力。

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.