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（如2017年飓风哈维）导致大量降雨及随之而来的径流与洪水。当径流与风暴潮相互作用时，所形成的洪水可能被显著放大，并产生无法通过简单叠加其各自来源来模拟的效应。为开发径流、风暴潮及复合洪水的精确数值模拟方法，我们提出了一种适用于修正浅水方程的局部间断伽辽金方法。在该修正中，连续性方程中引入了非零源项，利用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化结合了强稳定性保持显式龙格-库塔时间积分器。因此，通过CFL条件确保时间稳定性，并利用所开发方法的易并行特性，采用MPI并行化实现。我们通过一系列物理相关的数值试验验证了该方法的能力，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。结果凸显了所开发方法的守恒性质与鲁棒性，并展示了采用该方法进行复合洪水模拟的潜力。