## Wednesday, December 31, 2014

### What does Percent Not Converging Mean in SWMM5?

"SWMM 5's Routing Time Step Summary is your window into the model's heart, offering valuable insights with each pulse of data 🌟📈:

• Minimum Time Step: How swiftly the model can adapt to change, with a record speed of just 0.52 seconds! ⏱️✨
• Average Time Step: Balancing precision and performance, the model averages a comfortable 8.76 seconds. 🔄
• Maximum Time Step: Never missing a beat, the maximum cap is a steady 10.00 seconds. ⏳
• Percent in Steady State: A tranquil sea with 0.00% time in a steady state, reflecting constant motion. 🌊
• Average Iterations per Step: A modest 2.14 iterations, showcasing the model's efficiency. 🔄
• Percent Not Converging: Only 1.69% of the time, the model's predictions and reality don't quite align. 🛠️

Figure 1 illuminates the maximum trials per time step. This number reflects the model's persistence in seeking convergence during dynamic wave routing. 🌐🔍

Convergence in the Dynamic Wave Solution:

• The dance of calculation continues until the steps match the maximum number of trials. 🕺💃
• At each time step, the flows and depths are reassessed. If all nodes agree within the head tolerance, the iteration halts. 👍
• A single non-convergent node increments the Non-Converge Count, a rare occurrence. 📊
• Efficiency tip: Links that can be bypassed are noted, speeding up the process when dynamic wave calculations are unnecessary. 🏎️💨

With SWMM 5, you're not just running a model; you're conducting an orchestra of data where each note is a time step, each rest a chance to converge, and the symphony is the fluid mechanics of urban water systems. 🎼🌆"

*************************
Routing Time Step Summary
*************************
Minimum Time Step           :     0.52 sec
Average Time Step           :     8.76 sec
Maximum Time Step           :    10.00 sec
Percent in Steady State     :     0.00
Average Iterations per Step :     2.14
Percent Not Converging      :     1.69

 Figure 1.  Maximum number of trials per time step

In the dynamic world of SWMM 5, the Routing Time Step Summary serves as a crucial indicator of model stability and efficiency 🌐🔧. Here's a snapshot:

• Percent Non-Converging: This is the fraction of time when at least one element in the model's intricate network didn't align within the set number of trials per step. It's the ratio of the total non-convergent steps to the overall number of steps taken during the simulation 🔍💡.

• Dynamic Wave Solution Mechanics: Like a conductor leading an ensemble, the program meticulously iterates until the number of steps aligns with the maximum trials allowed. Each step is a note, each calculation a beat 🎶🧮.

• Convergence: It's a delicate balance. If all node depths settle within the accepted variance (below the head tolerance) after more than one step, the model ceases iterations. Harmony is achieved ✅🔄.

• Non-Convergence: However, should even a single node remain unresolved, the Non-Converge Count ticks up, a rare but noted event in the symphony of simulation 🚦📊.

• Efficiency: Not every link needs a detailed calculation at each step. By identifying which can be bypassed, the program conserves energy, speeding up like a swift current bypassing a tranquil pool 🏎️💨.

Figure 2 likely illustrates this concept further, capturing the essence of a model that is both robust and refined. By understanding these dynamics, you can ensure a smoother, more accurate simulation, leading to more reliable predictions and planning in urban water systems 🌟🌊.

 Figure 2.  Link Bypass is based on the Upstream and Downstream Nodes

// --- keep iterating until convergence
while ( Steps < MaxTrials )
{
// --- execute a routing step & check for nodal convergence
initNodeStates();
converged = findNodeDepths(tStep);
Steps++;
if ( Steps > 1 )
{
if ( converged ) break;

// --- check if link calculations can be skipped in next step
}
}
if ( !converged ) NonConvergeCount++;

//  --- identify any capacity-limited conduits