Open Channel Flow - Sediment Transport in Irrigation Canals: A New Approach - page 39

The solution of the de St. Venant equations is complicated, also for
simple rectangular channels. General solutions are only possible by using
one of the numerical methods (see Table 2.7). The method with finite
differences is the most common one. The method of characteristics is
adequate for waves due to sudden gate operations. The finite element
method can accommodate canals with irregular boundaries.

Table 2.7. Summary of the methods to solve the de St. Venant equations.

de St. Venant Equations

Numerical Methods

Finite
element Approximate

Direct Method of characteristics method Methods

Implicit Explicit Characteristic nodes Rectangular grid Storage routing

Implicit Explicit Implicit Explicit Muskingum

Diffusion analogy
Kinematic wave

The solution method of the various numerical procedures can be
explicit or implicit:
•

Explicit: the discharge Q and water depth y at the next time-step are
expressed in terms of the discharge Q and water depth y at the current
time step; this method is straightforward, but it must be in line with
the Courant stability criterion ( c ( t / x ) < 1). This criterion imposes a
severe limitation on the time-distance grid.

• Implicit: the discharge Q and water depth y are related to subsequent

and previous time steps, which is a more complex solution procedure,
but a stable one.

2.11 RECTANGULAR CHANNELS AND THE METHOD
OF CHARACTERISTICS

The curvature of the wave front of a gradually varied unsteady flow is mild
and the change in water depth is gradual. The vertical component of the
acceleration is negligible in comparison to the total acceleration; the effect
of the friction is significant and should not be neglected in the unsteady
flow analysis. In irrigation systems the occurrence of rapid varied flow
should be prevented by a gradual operation of the regulating and control
structures.
One of the main advantages of the method of characteristics is the
possibility to visualize the way in which flow disturbances or the effects