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### The SWMM 4 Dynamic Wave Solution

The SWMM 4 Dynamic Wave Solution

The attached PDF file is a copy of Appendix C of the SWMM 4 manual explaining the three St Venant solutions in SWMM 4 / Extran 4.  The current SWMM 5 solution in its dynamic wave solution is an adaptive time step iterative solution of the ISOL Zero solution in SWMM 4.

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• SWMM 4 and SWMM 5 St. Venant Solutions Contrasted

1. Compute at time t+delta t the values of dQ/dt for the Links and dH/dt for the Nodes from the properties at time t
2 Iterate at least 2 times until either all nodes and links are converged or a maximum of 8 iterations are reached
3. Use the values of Q and H at time t+delta t for the new time step

The SWMM5 Solution for Flow and Depth at each time step.  The new depth and new flow is always based on the old depth and old flow and normally converges fast as the flow is gradually varied.   The solution is iterative and implicitly uses the new depth and flow at each iteration.

The SWMM4 Solution for Flow and Depth is solved Explicitly at each time step.  The new depth and new flow is always based on the old depth and old flow and and a half and full time step during the time step.

• The SWMM 4 Dynamic Wave Solution for ISOL=0

The attached PDF file is a copy of the Extran 3 solution in the  SWMM 4 manual explaining the ISOL=0 solution in SWMM 4 / Extran 4.  The current SWMM 5 solution in its dynamic wave solution is an adaptive time step iterative solution of the ISOL=0 solution in SWMM 4.