
88 Modeling shallow water ows using the DG method
Following Garcia-Navarro and Vazquez-Cendon (2000), the Roe’s
ux for the Saint Venant equations for nonrectangular channels is given
by Equation (5.24), where the variables in the equation are dened by
Equations (5.25) to (5.29). As pointed out before, the shallow water ow
is governed by the eigenvalues of the Saint Venant equations given by
Equations (5.5) and (5.6), and represent physical characteristics of the ow.
The choice of the equation modeled should not affect the eigenvalues.
Thus, the wave speeds in Equations (5.21) and (5.26) are approximated
with the eigenvalues given by Equation ...