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Modeling Shallow Water Flows Using the Discontinuous Galerkin Method
book

Modeling Shallow Water Flows Using the Discontinuous Galerkin Method

by Abdul A. Khan, Wencong Lai
March 2014
Intermediate to advanced content levelIntermediate to advanced
215 pages
5h 59m
English
CRC Press
Content preview from Modeling Shallow Water Flows Using the Discontinuous Galerkin Method
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 specied otherwise.
i
λ
=
1
2
()
1
2
||
1
3
FF+F
nK
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
xy
xx yy xy
(7.25)



λ=
+−
λ= +
λ=
++
1
2
3
un vn c
un vn
un vn c
xy
xy
xy
(7.26)




=−
=−
=+
+
1
,
0
,
1
123
KKKucn
vcn
cn
cn
ucn
vc ...
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Publisher Resources

ISBN: 9781482226010