This research is aimed at achieving an efficient digital infrastructure for evaluating risks and damages caused by tsunami flooding. It is mainly focused on the suitable modeling of debris dynamics for a simple (but accurate enough) assessment of damages. For different reasons including computational performance and Big Data management issues, we focus our research on Eulerian debris flow modeling. Rather than using complex multiphase debris models, we rather use an empirical transportation and deposition model that takes into account the interaction with the main water flow, friction/contact with the ground but also debris interaction. In particular, for debris interaction, we have used ideas coming from vehicular traffic flow modeling. We introduce a velocity regularization term similar to the so-called ``anticipation term'' in traffic flow modeling that takes into account the local flow between neighboring debris and makes the problem mathematically well-posed. It prevents from the generation of ``Dirac measures of debris'' at shock waves. As a result, the model is able to capture emerging phenomenons like debris aggregation and accumulations, and possibly to react on the main flow by creating hills of debris and make the main stream deviate. We also discuss the way to derive quantities of interest (QoI), especially ``damage functions'' from the debris density and momentum fields. We believe that this original unexplored debris approach can lead to a valuable analysis of tsunami flooding damage assessment with Physics-based damage functions. Numerical experiments show the nice behaviour of the numerical solvers, including the solution of Saint-Venant's shallow water equations and debris dynamics equations.

中文翻译：

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浅水Saint-Venant方程和碎屑运输-沉积模型的有效求解器

这项研究旨在建立一个有效的数字基础设施，以评估海啸洪水造成的风险和破坏。它主要关注于碎片动力学的适当建模，以简单（但足够准确）地评估损害。由于各种原因，包括计算性能和大数据管理问题，我们将研究重点放在欧拉泥石流建模上。与其使用复杂的多相碎屑模型，不如使用经验性的运输和沉积模型，该模型考虑了与主要水流的相互作用，与地面的摩擦/接触以及杂物的相互作用。特别是对于杂物交互作用，我们使用了来自车辆交通流建模的想法。我们引入了一个速度正则项，类似于所谓的``期望项'' 在交通流建模中，该模型考虑了相邻碎片之间的局部流，并在数学上很好地解决了问题。它可以防止在冲击波时产生``狄拉克碎片措施''。结果，该模型能够捕获新出现的现象，例如碎片聚集和聚集，并可能通过创建碎片堆并使主流偏离而对主流产生反应。我们还讨论了从碎屑密度和动量场得出感兴趣量（QoI）的方法，特别是``损伤函数''。我们相信，这种原始的未探索的碎片方法可以通过基于物理的破坏函数对海啸洪水破坏评估进行有价值的分析。数值实验表明数值求解器具有良好的性能，