Notes on RKDG Methods for Shallow-Water Equations in Canal Networks

Abstract

PDE models for network flows are used in a number of different applications, including modeling of water channel networks. While the theory and first-order numerics are well developed, high-order schemes are not well developed. We propose a Runge---Kutta discontinuous Galerkin method as an efficient, effective and compact numerical approach for numerical simulations of 1-D models for water flow in open canals. Our numerical tests show the advantages of RKDG over first-order schemes.