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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
41Chapter three: DG method for 1D nonconservative equations
∫∫
+
=()
ˆ
()
ˆ
0NxqdxNx
C
x
dx
i
x
x
i
x
x
s
e
e
e
s
e
e
e
(3.44)
∫∫
+−
=() () ()
()
() 0NxNxdx qNxC
Nx
x
Nxdx C
ij
x
x
ji
x
x
i
j
x
x
j
s
e
e
e
s
e
e
e
s
e
e
e
(3.45)
ξξξ
∂ξ
∂ξ
ξξ
=
2
() () ()
()
() 0
1
1
1
1
1
1
x
NNdqNC
N
NdC
ij ji
i
jj
(3.46)
+
−−
=
2/61/6
1/62/6
1/21/2
1/21/2
0
0
1
2
1
2
1
2
x
q
q
C
C
C
C
(3.47)
=
−−
1
33
33
1
42
24
1
2
1
2
1
2
q
q
x
C
C
x
C
C
(3.48)
A similar procedure as described above for Equation (3.41) is adopted
for Equation (3.42), and the results are given by Equations (3.49) to (3.53). In
Equation (3.54), the numerical uxes are c ...
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Publisher Resources

ISBN: 9781482226010