v(ex)
v(in)
ni
e
A typical element e and its neighboring element along edge i with normal ni; v(in) and v(ex) denote
Fig. 2:
the value of a function v along edge i when approaching the edge from the interior and exterior of the
element respectively.
3.
NUMERICAL MODEL
In
this
section,
we
give
a
detailed
description
of
our
DG
sediment
transport/morphological model. To begin we define some notation. Given a spatial domain, Ω,
which has been discretized into a set of non-overlapping elements, let Ωe define the domain of a
typical element e and denote the boundary of the element by Γe . Our numerical approximation of
z will make use of piecewise smooth functions which are continuous over Ωe but which allow
discontinuities between elements along a given edge. We denote this space of functions by Vh.
(in)
Given a smooth function v defined over e, we denote the values of v along an edge by v
when
(ex)
approaching the edge from the interior of the element and v
when approaching the edge from
the exterior of the element. The outward unit normal vector for the boundary of the element will
be denoted by n, and the fixed unit normal vector for a given edge i will be denoted by ni (see
Fig. 2).
In our numerical scheme, we will also make use of continuous, piecewise linear
approximations of U and ζ obtained from the ADCIRC model to compute the local sediment
transport rates.
Briefly, these approximations are obtained by solving the shallow water
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