How to Decide on a Time Step in InfoSWMM, ICM SWMM, or SWMM5

 How to Decide on a Time Step in InfoSWMM, ICM SWMM, or SWMM5

Understanding the Problem:

• Time Step Importance: The time step (also called the routing time step or computational time step) is a crucial parameter in dynamic hydraulic simulations. It determines how often the model calculates flow and depth in each element (links and nodes) of the network.
• Continuity Error: This error reflects the degree to which mass is conserved in the model. Ideally, the amount of water entering and leaving the system, plus any changes in storage, should balance out perfectly. A large continuity error indicates a problem with the simulation.
• Unstable Links: Unstable links exhibit rapid, unrealistic oscillations in flow or depth, often caused by an inappropriate time step or other model setup issues.

The Iterative Approach to Time Step Selection:

Step 1: Initial Guess and Evaluation

• Initial Guess (300 seconds): A 5-minute time step is a common starting point for some models, but as you found, it can be too large for systems with rapid changes in flow or complex hydraulics.
• Large Continuity Error and Instability: A large time step often leads to these problems because it cannot accurately capture the fast-paced changes in the system. The simulation essentially "skips over" important hydraulic events.
• Average Time Step as a Guide: The "average time step" reported by the simulation (2.6 seconds in your case) is a very useful indicator. It's the average time step that the model's internal variable time-step algorithm determined was needed to maintain numerical stability during the simulation. A large discrepancy between your chosen fixed time step and this average suggests that your fixed time step is too large.

Step 2: Refinement Based on Average Time Step

• New Time Step (10 seconds): You wisely chose a new time step that is closer to the reported average time step but still slightly larger. Using a time step very close to the minimum can significantly increase simulation time. It is better to be closer to the average time step.
• Reduced Continuity Error and Stable Flows: By using a smaller, more appropriate time step, you improved the accuracy of the simulation. The model can now better resolve the hydraulic changes, leading to a smaller continuity error and eliminating the unstable link flows.

Why this approach works:

• Variable Time Step Logic: SWMM and related software often use a variable time-step algorithm internally, even if you specify a fixed time step for reporting results. This algorithm adjusts the time step during the simulation based on the rate of change in flow and depth to maintain stability.
• Average Time Step as a Proxy: The average time step reported by the model reflects the time step that was generally needed to keep the simulation stable using this variable time-step logic. It provides valuable insight into the appropriate time step for your specific model.
• Iterative Improvement: Finding the optimal time step is often an iterative process. You start with an initial guess, evaluate the results, and then adjust the time step based on the model's behavior.

Additional Tips and Considerations:

• Courant Condition: The Courant condition is a theoretical stability criterion that relates the time step to the flow velocity and the length of the links. While SWMM's internal algorithms handle this to some extent, it is important to be aware of it. For explicit solvers, it is expressed as:
  • Δt ≤ Δx / c
  • where Δt is the time step, Δx is the link length, and c is the wave celerity (approximately the flow velocity in open channels).
  • If your links are very short and your velocities are very high a smaller time step will be needed.
• Model Complexity: More complex models (e.g., those with many interconnected ponds, rapid changes in flow, steep slopes, or complex control structures) generally require smaller time steps.
• Simulation Time: Smaller time steps increase simulation time. You need to find a balance between accuracy and computational efficiency.
• Output Interval: The reporting time step (output interval) can be larger than the routing time step. You might route with a 10-second time step but only save results every 5 or 15 minutes.
• Sensitivity Analysis: It's good practice to perform a sensitivity analysis by running your model with a few different time steps (e.g., 5, 10, and 15 seconds) to see how much the results change. If the results are not significantly affected, you can use the larger time step to save time.
• Other Model Issues: Keep in mind that continuity errors and instability can also be caused by other issues, such as incorrect boundary conditions, errors in the network connectivity, or unrealistic parameters.

In summary, the iterative approach you've described, guided by the average time step reported by the simulation, is a sound method for finding a suitable time step in InfoSWMM, ICM SWMM, or SWMM5. This approach helps to improve the accuracy and stability of your simulations while maintaining reasonable computational efficiency.

Siphon Simulation in SWMM 5, ICM SWMM, PCSWMM and InfoSWMM

Siphon Simulation in SWMM 5, ICM SWMM, PCSWMM and InfoSWMM

 This is a great explanation of how siphons are simulated in SWMM 5 and InfoSWMM. Here's a breakdown of why this approach works and a few additional thoughts:

Why this approach to Siphon Simulation in SWMM 5 and InfoSWMM Works:

• Fundamental Principles: The simulation relies on the fundamental principles of fluid mechanics:
  • Continuity Equation: This ensures conservation of mass at each node. In simpler terms, what flows into a node must either flow out or be stored, leading to a change in depth.
  • Momentum Equation: This governs the flow within the links (pipes). It accounts for forces like gravity, pressure, and friction, which determine the velocity and flow rate.
• Numerical Solution: SWMM 5 and InfoSWMM employ numerical methods to solve these equations iteratively over time. Each time step, the model calculates the flow in each link and the depth at each node based on the previous time step's conditions and the specified inflows and boundary conditions.
• Simplified Representation: The siphon is not explicitly modeled as a separate element type. Instead, its behavior emerges naturally from the interaction of the nodes (manholes) and links (pipes) based on their physical properties (elevation, diameter, length, roughness) and the governing equations.
• Head Difference Drives Flow: As stated, the key to siphon initiation and operation is the head difference between upstream and downstream nodes. Once the upstream node (MH1 in your example) fills sufficiently, a head difference develops, driving flow through the siphon, even if part of the conduit is higher than the water level at the inlet.

Key Elements and How They Contribute:

1. Inflow: Provides the water that initiates the siphon action. Different inflow types accurately simulate various scenarios (dry weather, wet weather, constant flow, etc.).

2. Boundary Condition: Defines the downstream constraint. A free outfall allows unimpeded discharge, while a fixed or time-series outfall can simulate interaction with receiving water bodies or other hydraulic structures.

3. Node Properties (Invert, Max Depth, Surcharge Depth):

   • Invert: Defines the elevation of the bottom of the node, crucial for calculating head.
   • Max Depth: Represents the depth at which the node becomes full and potentially overflows or is pressurized.
   • Surcharge Depth: An optional depth above the max depth, simulating a pressurized condition. This is important when the water level rises above the crown of the pipe.

4. Link Properties (Length, Diameter, Offsets):

   • Length & Diameter: Determine the volume and flow capacity of the pipe.
   • Offsets: Define the elevation difference between the pipe invert and the node invert. These are crucial for accurate representation of the siphon's geometry.

5. Calculated Variables (Node Depths, Link Flows, Link Depths, Cross-sectional Areas): These are the outputs of the simulation, dynamically changing with each time step based on the input data and governing equations.

Additional Considerations and Potential Enhancements in SWMM 5 and InfoSWMM

• Entrance and Exit Losses: While the basic simulation captures the main siphon behavior, adding minor losses (entrance and exit losses) at the nodes connected to the siphon can improve accuracy, especially for high flow conditions. InfoSWMM allows for these loss coefficients to be input.

• Air Entrapment: In reality, air can become trapped in a siphon, potentially affecting its performance. SWMM 5 doesn't explicitly model two-phase flow (air and water), so this is a limitation. However, if significant air entrapment is expected in a real-world scenario, you might need to consider other modeling approaches or design modifications to ensure proper venting.

• Break-Siphon Conditions: Understanding under what conditions the siphon might "break" (cease to function as a siphon) is important. This usually happens when the upstream head is insufficient to maintain flow over the high point. The simulation can help you identify these critical conditions.

In conclusion, the described method effectively leverages the core capabilities of SWMM 5 and InfoSWMM to simulate siphon behavior without requiring specialized siphon elements. By accurately defining the node and link properties and applying appropriate inflows and boundary conditions, you can model the complex hydraulics of a siphon system and gain valuable insights into its performance under various operating conditions.