Recent tropical cyclones, e.g., Hurricane Harvey (2017), have lead to significant rainfall and resulting runoff with accompanying flooding. When the runoff interacts with storm surge, the resulting floods can be greatly amplified and lead to effects that cannot be modeled by simple superposition of its distinctive sources. In an effort to develop accurate numerical simulations of runoff, surge, and compounding floods, we develop a local discontinuous Galerkin method for modified shallow water equations. In this modification, nonzero sources to the continuity equation are included to incorporate rainfall into the model using parametric rainfall models from literature as well as hindcast data. The discontinuous Galerkin spatial discretization is accompanied with a strong stability preserving explicit Runge Kutta time integrator. Hence, temporal stability is ensured through the CFL condition and we exploit the embarrassingly parallel nature of the developed method using MPI parallelization. We demonstrate the capabilities of the developed method though a sequence of physically relevant numerical tests, including small scale test cases based on laboratory measurements and large scale experiments with Hurricane Harvey in the Gulf of Mexico. The results highlight the conservation properties and robustness of the developed method and show the potential of compound flood modeling using our approach.

翻译：近期热带气旋（例如2017年飓风哈维）引发了显著降雨及伴随径流导致的洪水。当径流与风暴潮相互作用时，洪水可能被极大放大，产生无法通过简单叠加各独立来源进行建模的效应。为实现径流、风暴潮及复合洪水的精确数值模拟，我们针对修正浅水方程提出了一种局部间断伽辽金方法。在该修正中，连续性方程中加入了非零源项，通过文献中的参数化降雨模型及后报数据将降雨纳入模型。间断伽辽金空间离散格式与强稳定性保持显式龙格-库塔时间积分器相结合，通过CFL条件确保时间稳定性，并利用所提方法的天然并行特性实现MPI并行化。我们通过一系列物理相关数值试验验证了该方法的性能，包括基于实验室测量的小尺度算例，以及墨西哥湾飓风哈维的大尺度实验。结果凸显了该方法的守恒特性与鲁棒性，展示了利用本方法进行复合洪水建模的潜力。