SWMM5's routing engine, decoded side by side

KINEMATIC WAVE vs DYNAMIC WAVE

One equation, two solvers: what each keeps, what each drops, and when it matters.

Dynamic Wave / bidirectional Kinematic Wave / downstream-only Upstream-propagating signal Unsupported condition Supported / coupled solution
Symbol key
A = flow area · Q = discharge · qL = lateral inflow per unit length · y = flow depth · Sf = friction slope · S0 = conduit slope · T = top width

The seven-panel breakdown

1 · The St. Venant pair

∂A/∂t + ∂Q/∂x = qL
∂Q/∂t + ∂(Q²/A)/∂x + gA·∂y/∂x + gA(Sf−S0) = 0
Conceptual one-dimensional Saint-Venant continuity and momentum equations — the basis for Dynamic Wave routing.

2 · What kinematic wave keeps

Sf = S0
Q = (K/n)·A·R2/3·S01/2
Continuity is still solved through time and along the conduit. Momentum reduces to the normal-flow closure, relating flow and area through Manning's equation (K=1.0 SI, K=1.486 US customary).

3 · The dropped terms, at a glance

✕ Local acceleration
✕ Convective acceleration
✕ Pressure-gradient force
✓ Bed slope balanced by friction
Show full equation
∂Q/∂t + ∂(Q²/A)/∂x + gA·∂y/∂x + gA(Sf−S0) = 0
→ Sf = S0
Local acceleration, convective inertia, and the pressure-gradient term all vanish. What remains balances friction against bed slope.

4 · Which way information travels

ckin = dQ/dA > 0
cdyn = V ± √(gA/T) — free-surface only
Kinematic wave has one characteristic, always downstream. Dynamic wave's second one — built from the free-surface celerity √(gA/T) — can point upstream: the physical carrier of backwater. Surcharged, closed-pipe flow instead uses SWMM's surcharge treatment (EXTRAN, or the optional Preissmann Slot in 5.2).

5 · Where the shortcut holds

steep slope · high-velocity · dendritic · no downstream control
The two methods can agree closely when backwater, pressurization, flow reversal, and downstream controls are insignificant.

6 · The loop it can't enter

split ratio unknown a priori
A path that rejoins downstream needs both branches solved at once — kinematic wave's one-pass sweep has nowhere to close the loop, though a user-defined FLOW_DIVIDER node can still split flow by a fixed rule.

7 · Dynamic wave, contrast

Successive conduit-flow and node-depth updates
Conduit flows and node depths are repeatedly updated across the network until the hydraulic convergence criterion is met, or the maximum trial count is reached.
RECOMMENDED QA CHECKS:
  • flow-routing continuity error
  • nonconverging nodes
  • time-step-critical elements
  • flow instability index
  • conduit lengthening
  • capacity-limited conduits
  • maximum d/D
  • surcharge duration
  • flooding volume
  • reverse flow
  • adverse slopes
  • network topology
Engine reference: dynwave.c · dwflow.c · kinwave.c · flowrout.c — EPA SWMM5
Docs: User's Manual 5.2 · Hydraulic Reference Manual · Hydraulic Addendum · Source repository

The practical difference: a backwater profile

Kinematic wave's normal-depth line can't see the elevated tailwater. Dynamic wave's profile curves up to meet it.

conduit invert depth tailwater surface normal depth (KW) backwater curve (DW) downstream distance →
Amber: kinematic wave holds a constant depth above the invert, blind to the downstream water level. Cyan: dynamic wave's depth diverges upward as it nears the tailwater.

Try it: toggle the momentum terms

Uncheck a term to drop it from the equation and see which solver you land on.

SWMM's actual inertial-term controls are KEEP / DAMPEN / IGNORE, not simple on/off — these checkboxes are a simplified illustration.

Scenario explorer

Pick a condition and see how each solver responds.

Kinematic wave

Dynamic wave

Routing-method advisor

Check anything that applies to your network.

Evidence: compare your own runs

Run the same model once with KINWAVE and once with DYNWAVE, then drop both .rpt files here. They're parsed locally in your browser — nothing is uploaded.

OutputKinematic WaveDynamic Wave
Routing method detected——
Peak conduit flow——
Maximum node depth——
Max hours surcharged——
Total flooding volume——
Flow routing continuity error——
Total elapsed time——
Reverse-flow volumes and flow-class fractions live in the binary .out file, not the text report — this table shows what the .rpt itself contains.

What SWMM won't tell you

A converged run is not the same as a correct one. A continuity error under 10% is necessary, not sufficient — a Dynamic Wave run can converge cleanly and still report implausible depths if the network itself is wrong. And once a network has been vetted against a Dynamic Wave run, switching to Kinematic Wave for long continuous-simulation or calibration work is a legitimate, and much faster, engineering choice — not a shortcut.

Term toggle, scenario explorer, and advisor are illustrative aids, not a hydraulic solver — always confirm with SWMM5 itself. The runs comparison reads your .rpt files locally in your browser.