SWMM - Computational Methods - Flow Routing

Flow routing within a conduit link in SWMM is governed by the conservation of mass and momentum equations for gradually varying, unstable flow (ie, the Saint Venant flow equations). The SWMM user can choose the level of sophistication used to solve these equations:

• Steady - constant flow, just sum the hydrographs
  Constant-flow routing represents the simplest type of routing possible (actually, no routing), assuming that within each computational time step the flow is uniform and stable. Thus, it simply translates inflow hydrographs at the upstream end of the conduit to the downstream end, with no delay or change in shape. The normal flow equation is used to relate flow rate to flow area (or depth).
  This type of routing cannot take into account channel storage, backwater effects, in/out losses, flow reversal, or pressurized flow. It can only be used with dendritic transport networks, where each node has only a single outflow link (unless the node is a Divider, in which case two outflow links are required). This form of routing is insensitive to the time interval employed and is, in fact, only appropriate for preliminary analyzes using long-term continuous simulations.
• Kinematic Wave - Considers uniform flow, without backwater or flooding. Considers only the effect of slope and friction, the others terms of the equation of motion are neglected
  This routing method solves the continuity equation along with a simplified form of the moment equation in each conduit. The latter assumes that the slope of the water surface is equal to the slope of the conduit.
  The maximum flow that can be carried through a conduit is the full normal flow value.
  Any flow in excess of that entering the inlet node is lost from the system or can accumulate on top of the inlet node and be reintroduced into the conduit as capacity becomes available.
  Kinematic wave routing allows flow and area to vary both spatially and temporally within a conduit.
  This can result in attenuated and delayed runoff hydrographs as the inflow is routed through the channel. However, this form of routing cannot take into account backwater effects, in/out losses, flow reversal or pressurized flow and is also restricted to dendritic network layouts. It can generally maintain numerical stability with moderately large time intervals, on the order of 1 to 5 minutes. If the effects mentioned above are not expected to be significant, this alternative can be an accurate and efficient routing method, especially for long-term simulations.
• Dynamic Wave - Complete Saint-Vennant Equations
  Dynamic Wave routing solves the complete one-dimensional Saint Venant flow equations and therefore produces the most theoretically accurate results.
  These equations consist of the continuity and moment equations for conduits and a volume continuity equation at the nodes.
  With this form of routing, it is possible to represent pressurized flow when a closed conduit becomes full, so flows can exceed the total normal flow value.
  Flooding occurs when the depth of water at a node exceeds the maximum available depth and excess flow is lost from the system or may accumulate at the top of the node and re-enter the drainage system.
  Dynamic wave routing can account for channel storage, back flow, in/out losses, flow reversal, and pressurized flow.
  By coupling the solution to both node water levels and conduit flow, it can be applied to any general network layout, even those containing multiple downstream bypasses and loops. It is the method of choice for systems subject to significant backwater effects due to downstream flow restrictions and with flow regulation through weirs and orifices.
  This generality comes at the price of having to use intervals of much shorter times, on the order of thirty seconds or less (SWMM can automatically reduce the user-defined maximum time interval as needed to maintain numerical stability).

Each of these routing methods employs the Manning equation to relate flow rate to flow depth and bed slope (or friction). For user-designated main power conduits, the Hazen-Williams or Darcy-Weisbach equation can be used when pressurized flow occurs.