
116 Modeling shallow water ows using the DG method
The second slope limiter (SL2) is adopted from Anastasiou and
Chan (1997). The variables are limited as given by Equation (6.20), where
∇U is the unlimited gradient given by Equation (6.15), r is a vector with
origin at the centroid of the element extending to any point within the
element, and ϕ is a chosen limiter given by Equation (6.21). To determine
the nodal values of the conserved variables, Equation (6.20) is evaluated
at the three nodes. The vector r for the node 1 will be
1
n
,
1
n
,
where
and
are the values at the center of the element. The param-
eters in Equation (6.21) are ex