A discontinuous Galerkin method for modeling flow in networks of channels

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

“…The Riemann solution at the junction consists of three waves separated by intermediate states u * 1 , u * 2 and u * 3 satisfying the junction conditions (33) and relations (16), i.e. the non-linear system…”

“…On the other side, high order numerics for network flows is a relatively newly developing one [11,13,16]. In [16], the authors apply RKDE method to treat flows in individual channels as a 1-D flows and use a 2-D junction region to couple them. In [13] the authors consider a local zooming of a T-junction, resulting in a two-dimensional flow problem at the canals' intersection, for which a high-order non-oscillatory method is applied.…”

“…On one side, a wealth of scientific works dealt with the problem of numerically simulating water flow in a single channel, see [18,22,25]. On the other side, high order numerics for network flows is a relatively newly developing one [11,13,16]. In [16], the authors apply RKDE method to treat flows in individual channels as a 1-D flows and use a 2-D junction region to couple them.…”

“…One reason for such interest can be found in rich set of applications ranging from vehicular traffic to supply chain and blood flow (see [2][3][4]9] for a fairly complete account of recent results). Within this research area, water channels networks (for irrigation or water distribution) is a quite richly investigated theme, see [10][11][12][13][14][15][16].…”

Entropy stable discontinuous Galerkin methods for nonlinear conservation laws on networks and multi-dimensional domains

“…Simulations over network-like domains can then be performed by coupling together 1D subdomains at junctions. This reduction from fully 2D or 3D simulations to simulations over 1D domains both simplifies the construction of meshes for network-like domains and reduces computational cost [1,2,3,4,5].…”