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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
59Chapter four: One-dimensional conservation laws
4.4.1 Shallow water ow equations in rectangular channels
The one-dimensional computational domain (x = [0, L]) is divided into
Ne elements; let
=<<< =
+
0
12 1
xx
xL
Ne
be a partition of the domain.
If
=≤
[,], 1Ix
xeNe
es
e
e
e
, then a discontinuous piecewise nite element
space of polynomials m is given by Equation (4.37). Inside an element,
the unknowns are approximated by Lagrange interpolation functions as
shown in Equation (4.38). The DG formulation for an element is given by
Equation (4.39). When the explicit time integration scheme is used, the
shallow water ow equations can be solved one by one ...
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Publisher Resources

ISBN: 9781482226010