As we enter the era of exascale computing, drastic changes in architectures have led to the emergence of a community of task-based runtimes. This talk presents the application of HPX, one such runtime, to the simulation of shallow water flows using finite elements. We will present an overview of the HPX runtime, its application to the parallelization of the discontinuous Galerkin finite element method, and sources of irregularity which can be taken advantage of for performance. Performance comparisons between an HPX implementation and a flat MPI parallelization will be shown for Stampede2's Knights Landing partition.