Hidden at first because they are far off the exact answer: HEC-RAS 7.0 2D SWE-ELM, HEC-RAS 7.0 SWE-EM, LISFLOOD-FP ACC, EPA SWMM 5.2.4, OpenSWMM 6 dynamic wave, Hydra, HydroNet finite volume, HydroNet FVM-PINN, SWMM 5.1.15, Landlab, HEC-RAS 6.6 previous release, HEC-RAS 6.6 2D SWE-EM. Click a name to show it.
Press play, or drag the slider, to watch the exact answer unfold. Models are compared at the end, t = 60 s.
Close-up of the front
The last stretch of the flood, 15 times taller. The dashed line is the exact front (where the last 5 % of the released water begins), the shaded band the 9.8 m allowed, and each triangle a model's front.
What happens
A 1-metre wall of water is released onto a dry, flat channel. It collapses into a wave whose front races over the dry ground at up to 6 m/s, thinning to a film at the tip, while a dip travels back into the reservoir.
Why it matters
Flood maps, evacuation times and dam-failure studies all depend on when water reaches dry land. A model that gets the front wrong gets the warning time wrong.
A good model must
put the flood front within 9.8 m of the exact one after 60 s (2.6 % of the distance it travels)
neither lose nor create water
get steadily more accurate on finer grids
How models did
In rank order: by each model's percent difference from the right answer, the largest over the test's accuracy checks (lower is better; results within 10 % of each other share a rank). Mass error, timing and NSE are shown beside it, not folded in. Each model runs the same inputs on 4 grids, from 10 m down to 1.25 m cells; the checks are scored on the 1.25 m grid, and each card lists the error on every grid. Compare them in the results viewer →
Since version 2 the front is measured by volume: the point beyond which the last 5 % of the released water lies. Version 1 used the 1 mm depth contour, which every production code missed by 12 to 211 m: on the thin tip a millimetre of depth moves that contour about 10 m, and production codes treat water shallower than about 1 mm as dry. The 1 mm edge is still reported, but no longer decides the result.
Basilisk
Basilisk (Popinet, basilisk.fr), its second-order well-balanced Saint-Venant solver on a uniform Cartesian grid with its defaults; Manning friction added as the usual semi-implicit term (it has none built in)
#1 0.45 % off
Rate the error shrinks on finer grids: 1 (90 % range 1 to 1.1); the method's expected rate is 0.8 or more
Run time, finest grid: 0.07 s· Intel(R) Xeon(R) 6973P-C, 2 cores, 15.6 GB, Linux 6.17.0-1022-azure (GitHub Actions (github-hosted, ubuntu24))
Settings: basilisk saint-venant.h (uniform Cartesian grid, defaults; a C program per test, generated by scripts/run_basilisk.py)
Flood front
• 1.68 m behind exact
0.45 % of the 376 m the exact front travels in 60 s
Leading edge (1 mm deep)
· 13.6 m from exact
reported, not counted · 3.8 % of the 358 m the exact 1 mm contour travels in 60 s
The script writes a small Basilisk C program for the test (kept in the model files below) and compiles it with qcc.
The test itself (inputs, exact answer, checks): A1F-010.zip. Check the score card with benchmark1d2d verify-card: its signature by the suite's public development key shows the card has not changed since it was written, not who wrote it.
Demo 1D
Worked example that ships with the suite: plain, well-understood schemes
#2= 0.52 % off
Rate the error shrinks on finer grids: 0.94 (90 % range 0.94 to 0.95); the method's expected rate is 0.8 or more
Flood front
• 1.95 m behind exact
0.52 % of the 376 m the exact front travels in 60 s
Leading edge (1 mm deep)
· 1.15 m from exact
reported, not counted · 0.32 % of the 358 m the exact 1 mm contour travels in 60 s
The model files for this run will be published with its next run.
The test itself (inputs, exact answer, checks): A1F-010.zip. Check the score card with benchmark1d2d verify-card: its signature by the suite's public development key shows the card has not changed since it was written, not who wrote it.
ANUGA
ANUGA 4.0.1 (Geoscience Australia / ANU), default settings on a triangular mesh
#2= 0.55 % off
Rate the error shrinks on finer grids: 0.9 (90 % range 0.89 to 0.91); the method's expected rate is 0.8 or more
Run time, finest grid: 6.2 s· AMD EPYC 7763 64-Core Processor, 2 cores, 15.6 GB, Linux 6.17.0-1022-azure (GitHub Actions (github-hosted, ubuntu24))
Settings: anuga (rectangular_cross mesh, defaults, sampled at cell centres)
Flood front
• 2.09 m behind exact
0.55 % of the 376 m the exact front travels in 60 s
Leading edge (1 mm deep)
· 12.4 m from exact
reported, not counted · 3.5 % of the 358 m the exact 1 mm contour travels in 60 s
The model files for this run will be published with its next run.
ANUGA builds its mesh and boundaries in Python: the script is the model.
The test itself (inputs, exact answer, checks): A1F-010.zip. Check the score card with benchmark1d2d verify-card: its signature by the suite's public development key shows the card has not changed since it was written, not who wrote it.
OpenSWMM 6
OpenSWMM Engine v6 with its new explicit finite-volume routing (FLOW_ROUTING FV): one cell per conduit on the channel tests, its default cells per pipe on the drainage networks
#4= 0.88 % off
Rate the error shrinks on finer grids: 0.66 (90 % range 0.54 to 0.77); the method's expected rate is 0.8 or more
Run time, finest grid: 0.68 s· INTEL(R) XEON(R) PLATINUM 8573C, 2 cores, 15.6 GB, Linux 6.17.0-1022-azure (GitHub Actions (github-hosted, ubuntu24))
Settings: swmm (FV routing, conduit per grid cell)
Flood front
• 3.33 m behind exact
0.88 % of the 376 m the exact front travels in 60 s
Leading edge (1 mm deep)
· 44.9 m from exact
reported, not counted · 13 % of the 358 m the exact 1 mm contour travels in 60 s
reported, not counted · the checks above are scored on the 1.25 m grid
Improves with finer grids
· rate 0.66 (90 % range 0.54 to 0.77)
reported, not counted · the scheme's design order is 1
3.3 m behind the exact front, where dynamic wave is 41 m behind, and it conserves water. The error shrinks at a rate of 0.66 (90 % range 0.54 to 0.77), below the design order of 1.
The test itself (inputs, exact answer, checks): A1F-010.zip. Check the score card with benchmark1d2d verify-card: its signature by the suite's public development key shows the card has not changed since it was written, not who wrote it.
GeoClaw
GeoClaw 5.9.2 (Clawpack), with its stock example's settings on a uniform grid
#4= 0.93 % off
Rate the error shrinks on finer grids: 0.7 (90 % range 0.51 to 0.89); the method's expected rate is 0.8 or more
Run time, finest grid: 2.2 s· AMD EPYC 9V74 80-Core Processor, 2 cores, 15.6 GB, Linux 6.17.0-1022-azure (GitHub Actions (github-hosted, ubuntu24))
Settings: geoclaw (uniform grid, stock example settings)
Flood front
• 3.51 m behind exact
0.93 % of the 376 m the exact front travels in 60 s
Leading edge (1 mm deep)
· 61.1 m from exact
reported, not counted · 17 % of the 358 m the exact 1 mm contour travels in 60 s
The test itself (inputs, exact answer, checks): A1F-010.zip. Check the score card with benchmark1d2d verify-card: its signature by the suite's public development key shows the card has not changed since it was written, not who wrote it.
The test itself (inputs, exact answer, checks): A1F-010.zip. Check the score card with benchmark1d2d verify-card: its signature by the suite's public development key shows the card has not changed since it was written, not who wrote it.
The test itself (inputs, exact answer, checks): A1F-010.zip. Check the score card with benchmark1d2d verify-card: its signature by the suite's public development key shows the card has not changed since it was written, not who wrote it.
TELEMAC-2D
openTELEMAC-2D 9.1.1, run with its default finite-volume settings
#7 1.5 % off
Rate the error shrinks on finer grids: 0.69 (90 % range 0.64 to 0.73); the method's expected rate is 0.8 or more
Run time, finest grid: 8.8 s· AMD EPYC 7763 64-Core Processor, 2 cores, 15.6 GB, Linux 6.17.0-1022-azure (GitHub Actions (github-hosted, ubuntu24))
Settings: telemac2d (Selafin, centreline nodes)
Flood front
• 5.75 m behind exact
1.5 % of the 376 m the exact front travels in 60 s
Leading edge (1 mm deep)
· 39.3 m from exact
reported, not counted · 11 % of the 358 m the exact 1 mm contour travels in 60 s
reported, not counted · the checks above are scored on the 1.25 m grid
Improves with finer grids
· rate 0.69 (90 % range 0.64 to 0.73)
reported, not counted · the scheme's design order is 1
The front is 5.8 m behind the exact one and depths are within 1.4 mm on average. The error shrinks on finer grids at a rate of 0.69 (90 % range 0.64 to 0.73), below the scheme's design order of 1. The thin leading edge, 1 mm deep, lags further (39 m): it stays dry too long. HLLC and second-order settings did not change that.
The test itself (inputs, exact answer, checks): A1F-010.zip. Check the score card with benchmark1d2d verify-card: its signature by the suite's public development key shows the card has not changed since it was written, not who wrote it.
OpenSWMM 6
OpenSWMM Engine v6 (HydroCouple's SWMM 6, pre-release) with dynamic-wave routing
#9= 11 % off
Rate the error shrinks on finer grids: -0.25 (90 % range -0.82 to 0.32); the method's expected rate is 0.8 or more
Run time, finest grid: 5.0 s· INTEL(R) XEON(R) PLATINUM 8573C, 2 cores, 15.6 GB, Linux 6.17.0-1022-azure (GitHub Actions (github-hosted, ubuntu24))
Settings: swmm (DYNWAVE routing, conduit per grid cell)
Flood front
• 41.2 m behind exact
11 % of the 376 m the exact front travels in 60 s
Leading edge (1 mm deep)
· 152 m from exact
reported, not counted · 43 % of the 358 m the exact 1 mm contour travels in 60 s
reported, not counted · the checks above are scored on the 1.25 m grid
Improves with finer grids
· rate −0.25 (90 % range −0.82 to 0.32)
reported, not counted · the scheme's design order is 1
Identical, number for number, to EPA SWMM 5.2.4: OpenSWMM 6 keeps the original dynamic-wave solver, including the 9 m one-conduit spike near x = 1,126 m.
The test itself (inputs, exact answer, checks): A1F-010.zip. Check the score card with benchmark1d2d verify-card: its signature by the suite's public development key shows the card has not changed since it was written, not who wrote it.
SWMM 5.1.15
EPA SWMM 5.1.15, the release before 5.2: on the parity tests compared with SWMM 5.2.4, on the exact tests scored like any other engine
#9= 11 % off
Rate the error shrinks on finer grids: -0.25 (90 % range -0.82 to 0.32); the method's expected rate is 0.8 or more
Run time, finest grid: 4.9 s· INTEL(R) XEON(R) PLATINUM 8573C, 2 cores, 15.6 GB, Linux 6.17.0-1022-azure (GitHub Actions (github-hosted, ubuntu24))
Settings: swmm (DYNWAVE routing, conduit per grid cell)
Flood front
• 41.2 m behind exact
11 % of the 376 m the exact front travels in 60 s
Leading edge (1 mm deep)
· 152 m from exact
reported, not counted · 43 % of the 358 m the exact 1 mm contour travels in 60 s
The test itself (inputs, exact answer, checks): A1F-010.zip. Check the score card with benchmark1d2d verify-card: its signature by the suite's public development key shows the card has not changed since it was written, not who wrote it.
EPA SWMM 5.2.4
EPA SWMM 5.2.4 with dynamic-wave routing; on the channel tests, the channel is written as one conduit per grid cell
#9= 11 % off
Rate the error shrinks on finer grids: -0.25 (90 % range -0.82 to 0.32); the method's expected rate is 0.8 or more
Run time, finest grid: 4.9 s· INTEL(R) XEON(R) PLATINUM 8573C, 2 cores, 15.6 GB, Linux 6.17.0-1022-azure (GitHub Actions (github-hosted, ubuntu24))
Settings: swmm (DYNWAVE routing, conduit per grid cell)
Flood front
• 41.2 m behind exact
11 % of the 376 m the exact front travels in 60 s
Leading edge (1 mm deep)
· 152 m from exact
reported, not counted · 43 % of the 358 m the exact 1 mm contour travels in 60 s
reported, not counted · the checks above are scored on the 1.25 m grid
Improves with finer grids
· rate −0.25 (90 % range −0.82 to 0.32)
reported, not counted · the scheme's design order is 1
SWMM's dynamic-wave routing is built for sewer networks, not dam breaks: the front is 41 m behind and the error does not shrink on finer grids. One conduit near x = 1,126 m also spikes to a 9 m depth at the reporting time (the chart clips it); that is the engine's own output, not a plotting fault.
The test itself (inputs, exact answer, checks): A1F-010.zip. Check the score card with benchmark1d2d verify-card: its signature by the suite's public development key shows the card has not changed since it was written, not who wrote it.
HEC-RAS 6.6
HEC-RAS 6.6 2D with its Eulerian shallow-water option (SWE-EM), the release before 7.0
#12= 15 % off
Rate the error shrinks on finer grids: -0.023 (90 % range -0.11 to 0.064); the method's expected rate is 0.8 or more
Run time, finest grid: 24.6 s· Intel(R) Xeon(R) Platinum 8370C CPU @ 2.80GHz, 2 cores, 16 GB, Windows 2025Server (GitHub Actions (github-hosted, win25-vs2026))
The test itself (inputs, exact answer, checks): A1F-010.zip. Check the score card with benchmark1d2d verify-card: its signature by the suite's public development key shows the card has not changed since it was written, not who wrote it.
HEC-RAS 7.0
HEC-RAS 7.0.1 2D with its Eulerian shallow-water option (SWE-EM), which HEC recommends for dam breaks
#12= 15 % off
Rate the error shrinks on finer grids: -0.021 (90 % range -0.11 to 0.065); the method's expected rate is 0.8 or more
Run time, finest grid: 19.5 s· AMD EPYC 9V45 96-Core Processor, 2 cores, 16 GB, Windows 2025Server (GitHub Actions (github-hosted, win25-vs2026))
The test itself (inputs, exact answer, checks): A1F-010.zip. Check the score card with benchmark1d2d verify-card: its signature by the suite's public development key shows the card has not changed since it was written, not who wrote it.
HEC-RAS 7.0
HEC-RAS 7.0.1 (US Army Corps of Engineers), built and run headless with its default settings; in 2D, its default full shallow-water option (SWE-ELM)
#14= 26 % off
Rate the error shrinks on finer grids: 0.083 (90 % range 0.053 to 0.11); the method's expected rate is 0.8 or more
Run time, finest grid: 19.5 s· AMD EPYC 9V45 96-Core Processor, 2 cores, 16 GB, Windows 2025Server (GitHub Actions (github-hosted, win25-vs2026))
The test itself (inputs, exact answer, checks): A1F-010.zip. Check the score card with benchmark1d2d verify-card: its signature by the suite's public development key shows the card has not changed since it was written, not who wrote it.
HEC-RAS 6.6
HEC-RAS 6.6, the release before 7.0, run the same way (1D, and 2D with its default SWE-ELM): kept so a change between versions shows
#14= 26 % off
Rate the error shrinks on finer grids: 0.083 (90 % range 0.053 to 0.11); the method's expected rate is 0.8 or more
Run time, finest grid: 23.8 s· Intel(R) Xeon(R) Platinum 8370C CPU @ 2.80GHz, 2 cores, 16 GB, Windows 2025Server (GitHub Actions (github-hosted, win25-vs2026))
reported, not counted · the checks above are scored on the 1.25 m grid
Improves with finer grids
· rate 0.08 (90 % range 0.05 to 0.11)
reported, not counted · the scheme's design order is 1
The flood advances as a steep bore and its front is 97 m behind the exact one; the error does not fall on finer grids. HEC-RAS 2D was built and run with no GUI step; the dam-break step was carried in by a restart file.
The test itself (inputs, exact answer, checks): A1F-010.zip. Check the score card with benchmark1d2d verify-card: its signature by the suite's public development key shows the card has not changed since it was written, not who wrote it.
Hydra
Hydra 17 (NEER AI, Rust): its urban-drainage engine on the SWMM data model, run through its CLI with default settings
#14= 27 % off
Rate the error shrinks on finer grids: 0.0083 (90 % range -0.22 to 0.24); the method's expected rate is 0.8 or more
Run time, finest grid: 6.4 s· INTEL(R) XEON(R) PLATINUM 8573C, 2 cores, 15.6 GB, Linux 6.17.0-1022-azure (GitHub Actions (github-hosted, ubuntu24))
Settings: swmm (DYNWAVE routing, conduit per grid cell)
Flood front
• 102 m behind exact
27 % of the 376 m the exact front travels in 60 s
Leading edge (1 mm deep)
· 211 m from exact
reported, not counted · 59 % of the 358 m the exact 1 mm contour travels in 60 s
The test itself (inputs, exact answer, checks): A1F-010.zip. Check the score card with benchmark1d2d verify-card: its signature by the suite's public development key shows the card has not changed since it was written, not who wrote it.
LISFLOOD-FP ACC
LISFLOOD-FP 8.3, the local-inertia solver it is best known for; it leaves out the advection term
#14= 28 % off
Rate the error shrinks on finer grids: 0.047 (90 % range 0.021 to 0.073); the method's expected rate is 0.8 or more
Run time, finest grid: 0.07 s· AMD EPYC 7763 64-Core Processor, 2 cores, 15.6 GB, Linux 6.17.0-1022-azure (GitHub Actions (github-hosted, ubuntu24))
reported, not counted · the checks above are scored on the 1.25 m grid
Improves with finer grids
· rate 0.05 (90 % range 0.02 to 0.07)
reported, not counted · the scheme's design order is 1
The local-inertia scheme leaves out the advection term, so it is not expected to get a dam break right; it is shown because it is what most LISFLOOD-FP users run.
The test itself (inputs, exact answer, checks): A1F-010.zip. Check the score card with benchmark1d2d verify-card: its signature by the suite's public development key shows the card has not changed since it was written, not who wrote it.
Landlab
Landlab 2.11 (CSDMS), its OverlandFlow component: the local-inertial 2D flood scheme of de Almeida et al. (2012), written independently in NumPy, with its defaults
#18 32 % off
Rate the error shrinks on finer grids: 0.034 (90 % range 0.027 to 0.042); the method's expected rate is 0.8 or more
Run time, finest grid: 0.12 s· AMD EPYC 7763 64-Core Processor, 2 cores, 15.6 GB, Linux 6.17.0-1022-azure (GitHub Actions (github-hosted, ubuntu24))
Settings: landlab.components.OverlandFlow (local inertial, defaults; a node per cell centre)
Flood front
• 119 m behind exact
32 % of the 376 m the exact front travels in 60 s
Leading edge (1 mm deep)
· 231 m from exact
reported, not counted · 65 % of the 358 m the exact 1 mm contour travels in 60 s
The model files for this run will be published with its next run.
Landlab models are built in Python: the script is the model.
The test itself (inputs, exact answer, checks): A1F-010.zip. Check the score card with benchmark1d2d verify-card: its signature by the suite's public development key shows the card has not changed since it was written, not who wrote it.
HydroNet
HydroNet (Penn State) — its differentiable Roe finite-volume solver (Heun RK2, CFL 0.3), the engine inside its FVM-PINN
#19 63 % off
Rate the error shrinks on finer grids: < 0.0001 (90 % range < 0.0001 to < 0.0001); the method's expected rate is 0.8 or more
Run time, finest grid: 2.2 s· AMD EPYC 7763 64-Core Processor, 2 cores, 15.6 GB, Linux 6.17.0-1022-azure (GitHub Actions (github-hosted, ubuntu24))
Settings: hydronet (fvm; HydroNet dam-break example settings, CFL 0.3; h_dry 0.0001 m)
Flood front
• 237 m behind exact
63 % of the 376 m the exact front travels in 60 s
Leading edge (1 mm deep)
· 359 m from exact
reported, not counted · 100 % of the 358 m the exact 1 mm contour travels in 60 s
reported, not counted · the checks above are scored on the 1.25 m grid
Improves with finer grids
· rate −0.00 (90 % range −0.00 to −0.00)
reported, not counted · the scheme's design order is 1
The dam never breaks: no water crosses onto the dry bed. HydroNet's Roe residual uses a fixed 1 cm dry threshold and, at a face between a wet and a dry cell, the wet cell's own flux, so still water next to dry ground feels no net force. The same happens below a 1 cm downstream layer. Mass is conserved because nothing moves.
The model files for this run will be published with its next run.
HydroNet's mesh and network are built in Python: the script is the model.
The test itself (inputs, exact answer, checks): A1F-010.zip. Check the score card with benchmark1d2d verify-card: its signature by the suite's public development key shows the card has not changed since it was written, not who wrote it.
HydroNet
HydroNet's FVM-PINN neural network, trained per grid with the recipe of its own dam-break example (64×5 network, 5000 Adam epochs)
#20 190 % off
Rate the error shrinks on finer grids: 0.13 (90 % range 0.0038 to 0.25); the method's expected rate is 0.8 or more
Settings: hydronet (pinn; HydroNet dam-break example settings, 5000 Adam epochs; h_dry 0.0001 m)
Flood front
• 713 m ahead of exact
190 % of the 376 m the exact front travels in 60 s
Leading edge (1 mm deep)
· 641 m from exact
reported, not counted · 179 % of the 358 m the exact 1 mm contour travels in 60 s
reported, not counted · the checks above are scored on the 1.25 m grid
Improves with finer grids
· rate 0.13 (90 % range 0.00 to 0.25)
reported, not counted · the scheme's design order is 1
The trained network spreads 0.3–0.4 m of water over the whole dry channel downstream, so its front is 713 m ahead of the exact one; it gains 3.3 % of the water, and the error grows on finer grids. Its own finite-volume engine, by contrast, never starts the flow.
The model files for this run will be published with its next run.
HydroNet's mesh and network are built in Python: the script is the model.
The test itself (inputs, exact answer, checks): A1F-010.zip. Check the score card with benchmark1d2d verify-card: its signature by the suite's public development key shows the card has not changed since it was written, not who wrote it.
Not run yet: TUFLOW, MIKE 21, Iber, BASEMENT, Delft3D FM
Technical details for reviewers Checks, reference, inputs, sources
Checks and why each limit was chosen
Check
Difference measured as a percentage of
Latest
Difference
Why this check
volume_front
volume_front_error of h · in the score
of the 376 m the exact front travels in 60 s
–
5 × the error of the suite's first-order reference scheme (demo 1D, Godunov/HLL: 1.95 m on the finest grid), scoring method 2, rule R7; since v3.0.0 (v2: two finest cells, 2.5 m). 9.8 m is 2.6 % of the 376 m the front travels in 60 s, about 1.6 s of arrival time. The front is the abscissa beyond which lies the last 5 % of the water downstream of the dam (exact: x0 + 2c0·t·(1 − 0.05^(1/3)) = 1237.4 m at 60 s). An integral of depth is well conditioned on the thin tip, where a depth contour is not; it is computed against the solver's own downstream volume, so mass errors do not leak into it.
front_position
front_position_error of h · reported, not counted
of the 358 m the exact 1 mm contour travels in 60 s
–
Reported, not gating (since v2.0.0). Exact iso-contour at h=0.001·h0 (~1358 m). On the thin tip a 1 mm depth error moves this contour about 10 m, and production codes treat depths under ~1 mm as dry, so it measures thin-film handling more than the front; the volume front gates instead.
mass
global_mass_error of volume · conservation, beside the score
already a percentage
–
Conservation property of continuous equations.
convergence
observed order of L1 error in h · reported, not counted
the design order, 1
–
Measured from the error on every refinement level, as in ASME V&V 20.
Reference
Exact solution from references.ritter.depth_velocity.
More figures
Exact, t = 0 s
Exact, t = 15 s
Exact, t = 30 s
Exact, t = 45 s
Exact, t = 60 s
Demo solver, t = 60 s
Exact solution at five instants; dots are the demo solver on its finest grid at the final time.
Promotion checklist
Only frozen tests have fixed inputs and answers. This list is computed from the manifest and the published score cards; the rules are in the method.
Instantaneous dam break of still water of depth \(h_0 = 1\,\mathrm{m}\) at
\(x_0 = 1000\,\mathrm{m}\) onto a dry frictionless bed. The exact inviscid
1D Saint-Venant solution is a left-going rarefaction and a wet/dry front that
advances as \(x_f(t) = x_0 + 2 t \sqrt{g h_0}\). At \(t = 60\,\mathrm{s}\)
with \(g = 9.81\,\mathrm{m\,s^{-2}}\) the front is at \(1375.8\,\mathrm{m}\).
Citation
Ritter, A. (1892). "Die Fortpflanzung der Wasserwellen."
Zeitschrift des Vereines Deutscher Ingenieure, 36(33), 947–954.
Report identifier: ZdVDI 36(33).
The gating front is integral: the abscissa beyond which lies the last 5 %
of the water downstream of the dam, exactly \(x_0 + 2c_0 t\,(1-0.05^{1/3})\)
= 1237.4 m at 60 s, within 2.5 m. Version 1 used the 1 mm depth contour
(~1358 m). On the thin tip that contour moves about 10 m per millimetre of
depth error, and production codes treat depths under ~1 mm as dry, so every
production code failed it by 12–211 m while their wave bodies were close. It
is still reported, but no longer gates.
Front limit (v3.0.0)
The volume front must lie within 9.8 m of the exact one: 5 × the error
of the suite's first-order reference scheme on the finest grid (1.95 m), the
rule R7 of scoring method 2.
Version 2 allowed two finest cells (2.5 m), a resolution-based limit that
failed production codes whose depths are within 1–2 mm of the exact answer
everywhere and whose front lags 3–6 m (1–1.5 % of the 376 m it travels).
Whether the error shrinks at the expected rate is judged separately
(Converges), and is needed for the Verified label.
Pitfalls
Wet/dry treatment and positivity-preserving fluxes dominate front error;
schemes that clip negative depths can lag the front systematically.
First-order Godunov methods typically achieve observed order \(\approx 1\)
in L1(\(h\)); do not expect second-order near the front.
Mass conservation must be measured against the continuous conserved volume
(including dry cells), not against a wet-only mask.
Mesh spacings must keep Courant number fixed across the refinement study
(fixed_courant: 0.5).
Sources
Ritter, A. (1892). Die Fortpflanzung der Wasserwellen. ZdVDI 36(33).
Test A1F-010_ritter_dry_bed_dambreak · version 3.0.0 · data licence analytic-public
