Geoscience Reference
In-Depth Information
Figure 8.5
Flow fluxes at interface between coarse and fine grids.
not provide an unique value for
U
fi
. A distribution has to be assumed to determine
U
fi
. As an approximation,
U
fi
may be first obtained using the linear (or quadratic)
interpolation of the velocity on the coarse grid. The interpolated quantity is denoted
as
U
fi
, which may not satisfy the mass conservation law. Then the flow velocity
on the fine grid is scaled so that the obtained total flux is
U
c
h
c
l
c
. Therefore,
U
fi
is
calculated by
i
max
U
fi
=|
U
fi
|
(
1
|
U
fi
|
U
c
h
c
l
c
)
h
fi
l
fi
(8.4)
i
=
The flow velocity on the fine grid determined using Eq. (8.4) satisfies the mass
conservation law, and its distribution is close to the interpolated one.
At the interface between two blocks, the conservation law for suspended load is
i
max
U
c
h
c
l
c
C
c
=
U
fi
h
fi
l
fi
C
fi
(8.5)
i
=
1
and that for bed load is
i
max
q
bc
l
c
=
q
bfi
l
fi
(8.6)
=
i
1
where
C
c
and
C
fi
are the suspended-load concentrations on the coarse and fine
grids, respectively; and
q
bc
and
q
bfi
are the bed-load transport rates per unit width
correspondingly.
Like the flow flux, the suspended-load concentration and bed-load transport rate
can be uniquely, conservatively obtained from the fine grid to the coarse grid, but the
