Dynamic Wave Routing and Node Time Steps in SWMM5

Dynamic Wave Routing and Node Time Steps in SWMM5

SWMM 5 uses dynamic wave routing to simulate the movement of water through the drainage system. This method solves complex hydraulic equations to accurately represent flow and water level fluctuations. Time steps are crucial in this process, as they dictate how often these equations are solved.

Node Time Step Calculation

The node time step in SWMM 5 is variable, meaning it adjusts throughout the simulation based on the conditions at each node. The formula used for this calculation considers:

• Maximum Depth: The difference between the crown elevation (top) and invert elevation (bottom) of the node. This represents the maximum possible water depth at the node.
• Last Time Step: The time step used in the previous calculation.
• Change in Depth: The difference in water depth at the node between the current and previous time steps.

Why Node Time Step Matters

• Accuracy: A smaller node time step increases the accuracy of water level calculations, especially during rapid changes in flow, such as at the start of a storm or when a surge enters a node.
• Stability: It helps maintain numerical stability in the model, preventing errors and unrealistic results.

Relationship to Link Time Step

• Typically Smaller: The node time step is generally much smaller than the link time step (which governs flow routing in conduits). This is because water level changes in nodes can be more rapid and sensitive than flow changes in conduits.
• Importance at Simulation Start: The node time step is most critical at the beginning of a simulation, especially when starting with an empty system (no hot start file). This is when the change in depth is most significant.
• Time Step Critical Elements: If the node time step becomes smaller than the link time step, it can limit the overall simulation time step. SWMM reports these "Time Step Critical Elements" to help identify potential bottlenecks in the model.

Practical Implications

Understanding the node time step helps in:

• Model Stability: Ensuring that the model can handle rapid changes in flow and water levels, especially during critical storm events.
• Computational Efficiency: Balancing accuracy and simulation time by allowing SWMM to adjust the time step dynamically based on the system's behavior.
• Model Diagnostics: Using the "Time Step Critical Elements" report to identify nodes that might require closer attention or model refinement.

By considering these factors, modelers can build more robust and reliable SWMM models for stormwater management and flood prediction.

Figure 1. Equations for the Node Time Step.

Figure 2.  Node Time Step is critical at the beginning of the simulation.

Posted 14 ye