  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.
