Implicit Time Weighting

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 summarized in the tables below.

Explicit and Implicit Time Weighting and Time Weight Parameters
Explicit: = 0.0	Only values from the previous time-step are used in the solution
Implicit:  = 0.5	The average of the old and new time-step values for R, V and A are used to solve for
Implicit:  > 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:  = 1.0	Only values from the new time-step are used in the solution

Time step and Iteration Symbols
N	Last time-step value at time t and first estimate of N + ½
N+1/2	Last iteration value estimate for time
N+1	New time-step value at time

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

Equation 20: