A discontinuous Galerkin method for modeling flow in networks of channels

Flow in a network of numerous channels is a complex phenomenon that cannot be adequately modeled by 1-D models. Despite this, it is a common practice to model flow in each channel with the 1-D St. Venant equations. These channels are coupled with each other by prescribing some interior boundary conditions, which are either too simplistic to reproduce the physics accurately or are computationally expensive. In this paper, we present a dimensionally heterogeneous approach to resolve these issues. We treat flows in individual channels as 1-D flows. These channels are coupled together at junctions using a 2-D junction region. We present a systematic numerical treatment of the 1-D and the 2-D shallow water equations in the framework of an RKDG method so that the coupling between the 1-D and the 2-D domains is natural, conservative and consistent with the numerical scheme. We verify the 1-D and the 2-D code via comparisons with different analytical solutions for a wide variety of cases. We establish the accuracy of our heterogeneous junction model by comparing the simulation results to experimental data and to the results obtained from other junction models.