4/98
SED2D-WES Version 4.3 Beta
Allen Teeter of the WES Hydraulics Laboratory has suggested that an equation of the form
(
)
De = Κ 1 Κ 2 D u + 10 -5 λ
*
2
(22)
where
λ = the element size
K1 and K2 = constants
This formulation is provided through the DD card, where the variables K1, K2 and K3 ( 10 -5 above) are specified.
Equations 20 through 22 differentiate between dispersion coefficients parallel and transverse to the
direction of flow. Since the coefficients in the present version of SED2D-WES apply in the x - and y - directions,
not necessarily in the flow directions, these equations can be used only as a guide.
Fortunately, in most applications, effective diffusion is smaller than convection by the calculated flow
velocities, so a wrong choice does not affect the results very much unless the chosen coefficient is far too large.
The best approach then is to use a moderately high value (say 50 m2/sec) during the first few runs, then reduce the
coefficients until the run becomes numerically unstable. This will allow the user to determine a range of values for
which the model gives a converged solution. The user can then perform sensitivity analyses to determine how the
solution changes as the effective diffusion is varied over this range. If the solution does not vary greatly then the
model is "insensitive" to this coefficient, and no further testing is needed. If the solution varies widely as this
coefficient is varied then the user must rely upon validation of the model against field measurements in order to
determine the appropriate values. If no field data is available for comparison, the user should use as small a value
as possible, effectively de-emphasizing the importance of these terms in the overall solution of the system of
equations.
The PE card provides a method of specifying the effective diffusion in an automatic fashion based on the
Peclet number:
λu
Pe =
De
If the user specifies the Peclet number, then the effective diffusion is
27
WORKING DRAFT
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