Floodplain Simulation (2D plan view)

Shallow-water flood wave in a river valley seen from above: Manning roughness, inflow hydrograph, levee breach and a town. Same solver as the 3D twin.

Switch to 3D

Presets

Playback

Things to try

  1. Pick Levee breach at the peak and watch the town fill from the breach; then pick Spring flood to see the levee hold.
  2. Lower Levee height to 1 m: the river overtops the crest instead of breaching it.
  3. Raise Floodplain roughness (forest): the wave slows and the peak at the gauge arrives later.
  4. Choose Breach the levee here in Tools and click the levee, or Place sandbags to raise the ground by 1 m.

Hydrology

Valley and levee (restarts)

Levee breach

Tools

Speed

Layers

Model check

The science

What is modelled

A river valley 3.8 km long with a meandering channel, a floodplain, a town behind a levee and a small hamlet on the unprotected bank. A flood wave enters upstream; the page solves the 2-D shallow-water (Saint-Venant) equations on a 112 x 70 grid (34 m cells) and draws the result as a plan map (the 3D twin draws the same model over a Blender-built landscape).

Equations

  • Mass: dh/dt + d(hu)/dx + d(hv)/dy = R - I (R = rain, I = infiltration).
  • Momentum: d(hu)/dt + d(hu² + g h²/2)/dx + d(huv)/dy = -g h dz/dx - g n² u|u| / h1/3, and the same for v.
  • Manning roughness n: channel 0.035, grass and crops about 0.045, forest 2.2 times that, town 0.08 (buildings are represented as extra roughness, not as solid blocks).
  • Inflow hydrograph: Q(t) = Qb + (Qp - Qb) [ (t/tp) exp(1 - t/tp) ]k, peak Qp at t = tp, sharpness k.
  • Levee breach: the crest cells over the breach width are lowered from crest height to natural ground in a smooth-step over the formation time. The erosion process itself is prescribed, not simulated.

Numerics

Finite volumes with an HLL (Einfeldt) flux and hydrostatic reconstruction, which keeps a lake at rest exactly at rest and handles wet/dry fronts without negative depths. Friction is applied semi-implicitly. The time step follows the CFL rule dt = 0.4 dx / max(|u| + sqrt(g h)). Double precision is used so mass can be audited.

Honest limits

  • First-order scheme on 34 m cells: levee crests are one cell wide and wave fronts are smoothed; this is a teaching model, not a flood-risk study.
  • No sediment transport, no bridge or culvert hydraulics (the bridge is scenery), no groundwater; infiltration is a constant rate.
  • Heights are exaggerated by the slider (default x4) and buildings and trees are drawn larger than life so they stay visible from a kilometre away.
  • The damage index uses an illustrative depth-damage curve (damage = (depth / 3 m)0.8, capped at 1, church counted double). It is not a loss estimate.

Independent checks (shown in the page)

  • Well-balanced test: lake at rest on random, partly dry ground stays still to round-off.
  • Manning test: a separate long channel reaches the analytic normal depth h = (q n / sqrt(S0))3/5.
  • Live mass balance of the running simulation: stored volume change equals inflow + rain - infiltration - outflow.
depth 05 m
Hydrograph: inflow, flow past the town, outflow, breach flow
Cross-section at the town gauge
Flooded area, houses and damage over time
River stage at the gauge versus bankfull and levee crest
Made with 🟠 Blender