SWMM5, or the Storm Water Management Model version 5, is a computational tool used for simulating and managing runoff quantity and quality from urban areas. One of its key features is the variable time step option, which allows the system to determine the Courant-Friedrichs-Lewy (CFL) time step needed for each time step in the simulation.
The Courant-Friedrichs-Lewy condition is a necessary condition for the stability of numerical solutions of partial differential equations that describe physical phenomena such as fluid dynamics. In simple terms, the CFL condition is a limit on the size of the time step that can be used in the numerical simulation based on the spatial step size and the speed at which changes propagate through the system.
When using the variable time step option in SWMM5, it is suggested to use a maximum time step that is 2 to 5 times bigger than the average time step during a simulation. This recommendation balances the need for computational efficiency (larger time steps require less computational time) with the need for accuracy (smaller time steps can more accurately capture rapidly changing conditions).
However, it's important to be aware that both too large and too small a time step can cause continuity errors in a rapidly changing Pump/Force Main (FM) network.
If the time step is too large, the model might miss important rapid changes in the system, leading to errors in the computed solution. This is often referred to as a "numerical diffusion" where the model smears out the changes over time and space.
Conversely, if the time step is too small, the model might become unstable due to the accumulation of numerical errors. This is often referred to as a "numerical dispersion" where the model introduces artificial oscillations.
Therefore, the choice of the time step in SWMM5 requires careful consideration. It must be sufficiently small to capture the important dynamics of the system, but not so small as to make the computations excessively time-consuming or unstable. The variable time step option is a powerful feature that helps to balance these requirements by allowing the engine to dynamically adjust the time step as needed based on the current conditions in the system.