Contrasting SWMM 4 and SWMM 5 St. Venant Solutions
Both SWMM 4 and SWMM 5 aim to solve for changes in flow (Q) and depth (H) over time using the St. Venant equations, but they do so in fundamentally different ways:
- Compute Changes:
- SWMM 4 & SWMM 5: Both models compute changes in flow (dQ/dt) for links and changes in depth (dH/dt) for nodes based on conditions at time t.
- Iteration for Convergence:
- SWMM 5: Uses an iterative method where:
- Iteration: At least 2 iterations are performed, with up to a maximum of 8, aiming for convergence of all nodes and links.
- Implicit Method: The solution is implicitly iterative, meaning that each new iteration uses the updated values of Q and H from the previous iteration within the same time step. This approach generally leads to faster convergence, especially for gradually varied flow conditions.
- SWMM 4:
- Explicit Method: Solves the equations explicitly, where:
- Half and Full Step: The new values of Q and H are calculated based on the conditions at the beginning of the time step (t) plus adjustments made halfway through (t + delta t/2) and at the end (t + delta t).
- No Iterative Convergence: Unlike SWMM 5, it doesn't iterate to convergence within each time step but computes directly from one step to the next.
- Utilizing New Values:
- SWMM 5: Once convergence is achieved or the maximum iteration limit reached, the values of Q and H at t + delta t are used for the next time step, ensuring that the new step starts with the most recent, converged values.
- SWMM 4: Directly uses the new values calculated explicitly for the next time step without further iteration within that step.
Key Differences:
- Stability and Accuracy:
- SWMM 5's implicit method tends to be more stable for a wider range of conditions, especially when dealing with rapidly changing or complex flow situations due to its iterative approach towards convergence.
- SWMM 4's explicit method can be computationally faster for simple, stable flow conditions but might require smaller time steps to maintain accuracy and stability in more complex scenarios.
- Computational Approach:
- SWMM 5's method involves more computational work per time step due to iteration but can handle more complex hydraulic behaviors like backwater effects or tidal influences more accurately.
- SWMM 4's method, while simpler, might need careful setting of time steps to avoid numerical instability, especially in systems with significant backwater or when flows are changing rapidly.
In summary, SWMM 5 offers a more robust and adaptable solution for modeling urban drainage systems with its iterative, implicit approach, while SWMM 4 provides a simpler, direct computation method that's adequate for less complex or more stable hydraulic conditions.
