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User Manual Delft- 1 D2D
02755
November, 2000
2 Background principles
2.1 Basic Equations used for 2D computation.
The following basic equations are used for the 2D computations.
+ 8(vh)
=
öt
öx
ay
öuöuÇu H
öu
+ u— + v— + g— + g— + auuI= 0
ay
8xCh
3t
5x
av g_+
aç
av + u 3v + v+
vIV
g+avvI=
0
ex ey
Oych
8t
where the following notation is used:
uvelocity in x-direction (mis)
vvelocity in y-direction_(mis)
Vvelocity: V12 + v2
water level above plane of reference (m)
CChezy coefficient (im/s)
ddepth below plane of reference (m)
htotal water depth: +d (m)
awall friction coefficient (1/m)
These equations describe unsteady two-dimensional shallow water flow.
The equation (1), the so-called continuity equation, ensures the conservation of fluid.
The equations (2) and (3) are the momentum equations. They consist of acceleration terms,
the horizontal pressure gradient terms, advective terms, bottom friction terms and wall
friction terms. These equations are non-linear and they are a subset of the well-known
shallow water equations, that describe water motion for which vertical accelerations are
small compared to horizontal accelerations (this applies to tidal flow, river flow, flood flow).
As opposed to the shallow water equations, equations 1-3 do not incorporate the turbulent
stress terms, accounting for the subgrid transfer of momentum in between gridcells. These
terms have been omitted because they are relatively unimportant for flood flow
computations, in order to save computational effort.
WL
1
delft hydraulics
2-