
126 Modeling shallow water ows using the DG method
The Roe ux for 2D shallow water ow equations (Wang and Liu,
2000) is given by Equation (7.24). The parameters of the Roe ux are given
by Equations (7.25) to (7.28). The HLLC numerical ux is adopted in the
following tests unless specied otherwise.
i
∑
λ
=
1
2
()–
1
2
||
1
3
FF+F
Roe
LR ii i
i
(7.24)
α=
−∆+∆ −+∆
α= ∆−∆−∆−∆
α=
∆
+∆ +∆ −+∆
2
1
2
1
[( )( )]
2
1
2
1
2
3
h
c
qn qn un vn h
c
qvhn quhn
h
c
qn qn un vn h
xx yy xy
yx
xx yy xy
(7.25)
λ=
λ= +
λ=
1
2
3
un vn c
un vn
un vn c
xy
xy
(7.26)
=−
−
=−
=+
+
1
,
0
,
1
123
KKKucn
vcn
cn
cn
ucn
vc ...