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A common point of discussion in the comparison of hydraulic models is explicit time weighting versus implicit time weighting. The meaning of explicit and implicit, and the and time step symbols are

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summarized in the tables below.


Explicit and Implicit Time Weighting and Time Weight Parameters
Explicit: Image Modified = 0.0
Only values from the previous time-step are used in the solution
Implicit: Image Modified = 0.5

The average of the old and new time-step values for R, V and A are used to solve for Image Modified

Implicit: Image Modified > 0.5
A weighted average of old and new time-step values are used in the simulation. Typical values of q are 0.55 to 0.85
Fully Implicit: Image Modified = 1.0
Only values from the new time-step are used in the solution
Time step and Iteration Symbols
Last time-step value at time t and first estimate of N + ½
N+1/2
Last iteration value estimate for time Image Modified
N+1
New time-step value at time Image Modified

As an example of using the time weighting parameter Image Modified, consider the calculation of the gradient head term in the dynamic flow equation:

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Equation20
Equation20
Equation 20:

Image Modified 

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