Does the model get the dip in the water surface over a bump in the bed right?
Test A1F-040 Delestre (2013) Version 1.0.0
Hidden at first because they are far off the exact answer: LISFLOOD-FP ACC, EPA SWMM 5.2.4, OpenSWMM 6 dynamic wave, Hydra, SWMM 5.1.15, Landlab. Click a name to show it.
What happens
Water flows steadily and calmly along a 25 m channel over a smooth 20 cm hump. The surface dips over the hump by an amount fixed exactly by conservation of flow and energy.
Why it matters
Weirs, sills, bridge piers and bed forms all change the water level this way. A model that gets the dip wrong gets every structure's backwater wrong.
A good model must
keep the average depth error under 5 mm
carry the same flow along the whole channel
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 3 grids, from 0.2 m down to 0.05 m cells; the checks are scored on the 0.05 m grid, and each card lists the error on every grid. Compare them in the results viewer →
The SWMM dynamic-wave engines (EPA SWMM 5.2.4, OpenSWMM v6 dynamic wave and Hydra) never settle on this frictionless channel with 10 and 5 cm conduits, even with a 0.0025 s routing step: depths swing by more than a metre. On 20 cm conduits SWMM 5.2.4 is within 8 mm on the subcritical case. OpenSWMM v6's finite-volume routing stays close on all four bump tests.
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 under 0.01 % off
Rate the error shrinks on finer grids: 2.2 (90 % range 1.9 to 2.4); the method's expected rate is 0.8 or more
Run time, finest grid: 3.6 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)
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-040.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-040.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-040.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
#2= 0.03 % off
Rate the error shrinks on finer grids: 0.99 (90 % range 0.99 to 1); the method's expected rate is 0.8 or more
Run time, finest grid: 28.3 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)
The test itself (inputs, exact answer, checks): A1F-040.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
#5 0.047 % off
Rate the error shrinks on finer grids: 0.97 (90 % range 0.94 to 1); the method's expected rate is 0.8 or more
Run time, finest grid: 3.8 min· AMD EPYC 7763 64-Core Processor, 2 cores, 15.6 GB, Linux 6.17.0-1022-azure (GitHub Actions (github-hosted, ubuntu24))
The test itself (inputs, exact answer, checks): A1F-040.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
#6 0.12 % off
Rate the error shrinks on finer grids: 0.94 (90 % range 0.69 to 1.2); the method's expected rate is 0.8 or more
Settings: anuga (rectangular_cross mesh, defaults, sampled at cell centres)
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-040.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
#7 28 % off
Rate the error shrinks on finer grids: 0.0021 (90 % range 0.00038 to 0.0039); the method's expected rate is 0.8 or more
Run time, finest grid: 16.9 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)
Average depth error
• 56 cm off
28 % of the exact profile's mean depth, 1.97 m
Average flow error
• 1.24 m²/s off
28 % of the 4.42 m²/s unit discharge
Error by grid (L1 h)
· 0.2 m: 0.557 · 0.1 m: 0.556 · 0.05 m: 0.555
reported, not counted · the checks above are scored on the 0.05 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 2
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-040.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
#8 64 % off
Rate the error shrinks on finer grids: -0.13 (90 % range -0.27 to 0.011); the method's expected rate is 0.8 or more
Run time, finest grid: 6.3 s· AMD EPYC 7763 64-Core Processor, 2 cores, 15.6 GB, Linux 6.17.0-1022-azure (GitHub Actions (github-hosted, ubuntu24))
The test itself (inputs, exact answer, checks): A1F-040.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= 174 % off
Rate the error shrinks on finer grids: -3.7 (90 % range -15 to 7); the method's expected rate is 0.8 or more
Run time, finest grid: 1.8 min· 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)
Average depth error
• 1.45 m off
74 % of the exact profile's mean depth, 1.97 m
Average flow error
• 7.71 m²/s off
174 % of the 4.42 m²/s unit discharge
Error by grid (L1 h)
· 0.2 m: 0.00809 · 0.1 m: 0.838 · 0.05 m: 1.45
reported, not counted · the checks above are scored on the 0.05 m grid
Improves with finer grids
· rate −3.74 (90 % range −14.50 to 7.01)
reported, not counted · the scheme's design order is 2
The test itself (inputs, exact answer, checks): A1F-040.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= 174 % off
Rate the error shrinks on finer grids: -3.7 (90 % range -15 to 7); the method's expected rate is 0.8 or more
Run time, finest grid: 1.8 min· 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)
Average depth error
• 1.45 m off
74 % of the exact profile's mean depth, 1.97 m
Average flow error
• 7.71 m²/s off
174 % of the 4.42 m²/s unit discharge
Error by grid (L1 h)
· 0.2 m: 0.00809 · 0.1 m: 0.838 · 0.05 m: 1.45
reported, not counted · the checks above are scored on the 0.05 m grid
Improves with finer grids
· rate −3.74 (90 % range −14.50 to 7.01)
reported, not counted · the scheme's design order is 2
The test itself (inputs, exact answer, checks): A1F-040.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
#11 199 % off
Rate the error shrinks on finer grids: -0.2 (90 % range -0.28 to -0.12); the method's expected rate is 0.8 or more
Run time, finest grid: 1.4 min· 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)
Average depth error
• 1.5 m off
76 % of the exact profile's mean depth, 1.97 m
Average flow error
• 8.79 m²/s off
199 % of the 4.42 m²/s unit discharge
Error by grid (L1 h)
· 0.2 m: 1.14 · 0.1 m: 1.29 · 0.05 m: 1.5
reported, not counted · the checks above are scored on the 0.05 m grid
Improves with finer grids
· rate −0.20 (90 % range −0.28 to −0.12)
reported, not counted · the scheme's design order is 2
The test itself (inputs, exact answer, checks): A1F-040.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
#12 236 % off
Rate the error shrinks on finer grids: -3.9 (90 % range -14 to 6.4); the method's expected rate is 0.8 or more
Run time, finest grid: 1.9 min· 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)
Average depth error
• 1.86 m off
94 % of the exact profile's mean depth, 1.97 m
Average flow error
• 10.4 m²/s off
236 % of the 4.42 m²/s unit discharge
Error by grid (L1 h)
· 0.2 m: 0.0086 · 0.1 m: 0.893 · 0.05 m: 1.86
reported, not counted · the checks above are scored on the 0.05 m grid
Improves with finer grids
· rate −3.88 (90 % range −14.16 to 6.41)
reported, not counted · the scheme's design order is 2
The test itself (inputs, exact answer, checks): A1F-040.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: HEC-RAS 7.0, GeoClaw, TUFLOW, MIKE 21, Iber, BASEMENT, Delft3D FM
A frictionless 25 m channel with a parabolic bump
\(z = 0.2 - 0.05 (x - 10)^2\) on \(8 < x < 12\) carries \(q = 4.42\) m²/s,
held at 2 m downstream. In steady flow the discharge is constant and so is
the Bernoulli head, so at every point the depth is the subcritical root of
\[ \frac{q^2}{2 g h^2} + h + z = \frac{q^2}{2 g h_{out}^2} + h_{out}, \]
found to \(10^{-14}\) m (references/swashes.py). The surface dips to
1.71 m over the crest. The run starts from still water at 2 m and lasts
300 s.
What it checks
The balance between the bed slope and the pressure gradient in moving water,
and that a steady state carries the same discharge everywhere.
Citation
Delestre, O., et al. (2013). SWASHES: a compilation of shallow water analytic
solutions for hydraulic and environmental studies. Int. J. Numer. Meth.
Fluids, 72(3), 269–300. doi:10.1002/fld.3741. Goutal, N., and Maurel, F.
(1997), EDF report HE-43/97/016/B.
Sources
Delestre, O., Lucas, C., Ksinant, P.-A., Darboux, F., Laguerre, C., Vo, T. N. T., James, F., Cordier, S. (2013). SWASHES: a compilation of shallow water analytic solutions for hydraulic and environmental studies. doi:10.1002/fld.3741
Goutal, N., Maurel, F. (1997). Proceedings of the 2nd workshop on dam-break wave simulation (EDF HE-43/97/016/B). www.irit.fr/swashes
Test A1F-040_swashes_bump_subcritical · version 1.0.0 · data licence analytic-public