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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
12 Modeling shallow water ows using the DG method
Figure2.4. For a 3-node quadratic element, the shape functions are given
by Equation (2.23) and are shown in Figure2.5, where x
i
(i = 1, 2, 3) is the
coordinate of a node. The corresponding quadratic variation of a variable
is shown in Figure2.6.
=
=
()
1
0
Nx
ij
ij
ji
(2.21)
=
=
()
()
1
2
12
2
1
21
Nx
xx
xx
Nx
xx
xx
(2.22)
2
U
1
U
2
x
1
Figure 2.4 1D linear variation of a variable in an element.
x
3
2 1
1.0
1.0
N
1
(x) N
2
(x) N
3
(x)
Figure 2.5 1D quadratic shape functions.
x
3
2 1
U
1
U
2
U
3
Figure 2.6 1D quadratic variation of a variable in an element.
13Chapter two: General formulation of the discontinuous Galerkin ...
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Publisher Resources

ISBN: 9781482226010