
180 Modeling shallow water ows using the DG method
rectangular channel of unit width is 1000 m long with a dam located at 500 m.
The initial conditions for the ow depth, velocity, and pollutant concentra-
tion are given by Equation (9.20). For the idealized dam-break problem, exact
solutions for water depth and ow rate can be found (Henderson, 1966). The
pollutant concentration is transported as a shock. The speed of the concen-
tration shock, u
C
, is given by Equation (9.21) (Audusse and Bristeau, 2003),
where subscripts L and R denote values upstream and downstream of the
dam, respectively. The values of c
L
and c
R
are given by Equation (9