OpenHydro Bench
Exact answer known1D · free surfaceCandidate

Flow speeding up over a hump

Does the model switch from calm to rapid flow at the right place?

Test A1F-041
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

With less water, the flow over the hump passes through critical depth at its top and races down the far side as fast, shallow flow, with no jump.

Why it matters

Control sections like this set water levels upstream of weirs and steep reaches. The switch to rapid flow is where many schemes struggle.

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 →

RankModelDifferenceLargest difference inRun time
1Basilisk Saint-Venant<0.01 %Average depth error3.1 s
2ANUGA 4.0.10.11 %Average depth error–
3OpenSWMM 6 finite volume0.13 %Average depth error28.1 s
4=LISFLOOD-FP 8.3 · DG20.17 %Average depth error39.0 s
4=LISFLOOD-FP 8.3 · FV10.17 %Average depth error8.3 s
6TELEMAC-2D openTELEMAC 9.10.39 %Average depth error3.3 min
7=LISFLOOD-FP 8.3 · ACC50 %Average depth error3.8 s
7=Landlab OverlandFlow52 %Average depth error9.8 s
9=OpenSWMM 6 dynamic wave165 %Average flow error1.3 min
9=Hydra urban drainage167 %Average flow error1.3 min
11=SWMM 5.1.15 previous release189 %Average flow error1.3 min
11=EPA SWMM 5.2.4 dynamic wave189 %Average flow error1.3 min

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 (90 % range 2 to 2); the method's expected rate is 0.8 or more

Run time, finest grid: 3.1 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)

Average depth error
• 0.021 mm off
<0.01 % of the exact profile's mean depth, 0.640 m
Average flow error
• < 0.0001 m²/s off
<0.01 % of the 1.53 m²/s unit discharge
Error by grid (L1 h)
· 0.2 m: 0.000346 · 0.1 m: < 0.0001 · 0.05 m: < 0.0001
reported, not counted · the checks above are scored on the 0.05 m grid
Improves with finer grids
· rate 2.02 (90 % range 2.00 to 2.04)
reported, not counted · the scheme's design order is 1

Scored with method 3.0 · Score card: Basilisk Saint-Venant (snapshot de851a91)

ANUGA
ANUGA 4.0.1 (Geoscience Australia / ANU), default settings on a triangular mesh
#2 0.11 % off

Rate the error shrinks on finer grids: 0.91 (90 % range 0.69 to 1.1); the method's expected rate is 0.8 or more

Settings: anuga (rectangular_cross mesh, defaults, sampled at cell centres)

Average depth error
• 0.68 mm off
0.11 % of the exact profile's mean depth, 0.640 m
Average flow error
• 0.00153 m²/s off
0.1 % of the 1.53 m²/s unit discharge
Error by grid (L1 h)
· 0.2 m: 0.00242 · 0.1 m: 0.00123 · 0.05 m: 0.000684
reported, not counted · the checks above are scored on the 0.05 m grid
Improves with finer grids
· rate 0.91 (90 % range 0.69 to 1.14)
reported, not counted · the scheme's design order is 1

Within 0.7 mm with the SWASHES downstream condition (0.66 m held while the outflow is subcritical); three grids leave its convergence rate's range wide (0.69 to 1.14). With a free (transmissive) outflow instead, ANUGA settled on a fully subcritical state 1.06 m deep, 0.39 m off.

Scored with method 3.0 · Score card: ANUGA 4.0.1

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
#3 0.13 % off

Rate the error shrinks on finer grids: 1 (90 % range 0.88 to 1.2); the method's expected rate is 0.8 or more

Run time, finest grid: 28.1 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)

Average depth error
• 0.85 mm off
0.13 % of the exact profile's mean depth, 0.640 m
Average flow error
• 0.00017 m²/s off
0.011 % of the 1.53 m²/s unit discharge
Error by grid (L1 h)
· 0.2 m: 0.00361 · 0.1 m: 0.00181 · 0.05 m: 0.000848
reported, not counted · the checks above are scored on the 0.05 m grid
Improves with finer grids
· rate 1.04 (90 % range 0.88 to 1.21)
reported, not counted · the scheme's design order is 1

Scored with method 3.0 · Score card: OpenSWMM Engine v6 finite volume (6.0.0a4.dev1)

LISFLOOD-FP DG2
LISFLOOD-FP 8.3, second-order discontinuous Galerkin solver
#4= 0.17 % off

Rate the error shrinks on finer grids: 0.93 (90 % range 0.91 to 0.95); the method's expected rate is 0.8 or more

Run time, finest grid: 39.0 s · AMD EPYC 7763 64-Core Processor, 2 cores, 15.6 GB, Linux 6.17.0-1022-azure (GitHub Actions (github-hosted, ubuntu24))

Settings: lisflood (dg2 solver, defaults; CPU, double precision)

Average depth error
• 1.1 mm off
0.17 % of the exact profile's mean depth, 0.640 m
Average flow error
• 0.000402 m²/s off
0.026 % of the 1.53 m²/s unit discharge
Error by grid (L1 h)
· 0.2 m: 0.00396 · 0.1 m: 0.00208 · 0.05 m: 0.00109
reported, not counted · the checks above are scored on the 0.05 m grid
Improves with finer grids
· rate 0.93 (90 % range 0.91 to 0.95)
reported, not counted · the scheme's design order is 1

Scored with method 3.0 · Score card: LISFLOOD-FP 8.3 DG2

LISFLOOD-FP FV1
LISFLOOD-FP 8.3, first-order finite-volume solver (full shallow-water equations)
#4= 0.17 % off

Rate the error shrinks on finer grids: 0.95 (90 % range 0.94 to 0.95); the method's expected rate is 0.8 or more

Run time, finest grid: 8.3 s · AMD EPYC 7763 64-Core Processor, 2 cores, 15.6 GB, Linux 6.17.0-1022-azure (GitHub Actions (github-hosted, ubuntu24))

Settings: lisflood (fv1 solver, defaults; CPU, double precision)

Average depth error
• 1.1 mm off
0.17 % of the exact profile's mean depth, 0.640 m
Average flow error
• 0.000402 m²/s off
0.026 % of the 1.53 m²/s unit discharge
Error by grid (L1 h)
· 0.2 m: 0.00407 · 0.1 m: 0.00211 · 0.05 m: 0.00109
reported, not counted · the checks above are scored on the 0.05 m grid
Improves with finer grids
· rate 0.95 (90 % range 0.94 to 0.95)
reported, not counted · the scheme's design order is 1

Scored with method 3.0 · Score card: LISFLOOD-FP 8.3 FV1

TELEMAC-2D
openTELEMAC-2D 9.1.1, run with its default finite-volume settings
#6 0.39 % off

Rate the error shrinks on finer grids: 0.94 (90 % range 0.93 to 0.94); the method's expected rate is 0.8 or more

Run time, finest grid: 3.3 min · 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)

Average depth error
• 2.5 mm off
0.39 % of the exact profile's mean depth, 0.640 m
Average flow error
• 0.000372 m²/s off
0.024 % of the 1.53 m²/s unit discharge
Error by grid (L1 h)
· 0.2 m: 0.00905 · 0.1 m: 0.00473 · 0.05 m: 0.00248
reported, not counted · the checks above are scored on the 0.05 m grid
Improves with finer grids
· rate 0.94 (90 % range 0.93 to 0.94)
reported, not counted · the scheme's design order is 1

Scored with method 3.0 · Score card: openTELEMAC-2D v9.1.1

LISFLOOD-FP ACC
LISFLOOD-FP 8.3, the local-inertia solver it is best known for; it leaves out the advection term
#7= 50 % off

Rate the error shrinks on finer grids: -0.12 (90 % range -0.32 to 0.08); the method's expected rate is 0.8 or more

Run time, finest grid: 3.8 s · AMD EPYC 7763 64-Core Processor, 2 cores, 15.6 GB, Linux 6.17.0-1022-azure (GitHub Actions (github-hosted, ubuntu24))

Settings: lisflood (acceleration solver, defaults; CPU, double precision)

Average depth error
• 32 cm off
50 % of the exact profile's mean depth, 0.640 m
Average flow error
• 0.585 m²/s off
38 % of the 1.53 m²/s unit discharge
Error by grid (L1 h)
· 0.2 m: 0.269 · 0.1 m: 0.303 · 0.05 m: 0.317
reported, not counted · the checks above are scored on the 0.05 m grid
Improves with finer grids
· rate −0.12 (90 % range −0.32 to 0.08)
reported, not counted · the scheme's design order is 1

Scored with method 3.0 · Score card: LISFLOOD-FP 8.3 ACC

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= 52 % off

Rate the error shrinks on finer grids: 0.042 (90 % range -0.11 to 0.2); the method's expected rate is 0.8 or more

Run time, finest grid: 9.8 s · AMD EPYC 7763 64-Core Processor, 2 cores, 15.6 GB, Linux 6.17.0-1022-azure (GitHub Actions (github-hosted, ubuntu24))

Settings: landlab.components.OverlandFlow (local inertial, defaults; a node per cell centre)

Average depth error
• 33 cm off
52 % of the exact profile's mean depth, 0.640 m
Average flow error
• 0.46 m²/s off
30 % of the 1.53 m²/s unit discharge
Error by grid (L1 h)
· 0.2 m: 0.351 · 0.1 m: 0.351 · 0.05 m: 0.331
reported, not counted · the checks above are scored on the 0.05 m grid
Improves with finer grids
· rate 0.04 (90 % range −0.11 to 0.20)
reported, not counted · the scheme's design order is 1

Scored with method 3.0 · Score card: Landlab 2.11.0 OverlandFlow

OpenSWMM 6
OpenSWMM Engine v6 (HydroCouple's SWMM 6, pre-release) with dynamic-wave routing
#9= 165 % off

Rate the error shrinks on finer grids: -0.27 (90 % range -1.8 to 1.2); the method's expected rate is 0.8 or more

Run time, finest grid: 1.3 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
• 53 cm off
82 % of the exact profile's mean depth, 0.640 m
Average flow error
• 2.52 m²/s off
165 % of the 1.53 m²/s unit discharge
Error by grid (L1 h)
· 0.2 m: 0.361 · 0.1 m: 0.579 · 0.05 m: 0.525
reported, not counted · the checks above are scored on the 0.05 m grid
Improves with finer grids
· rate −0.27 (90 % range −1.78 to 1.23)
reported, not counted · the scheme's design order is 1

Scored with method 3.0 · Score card: OpenSWMM Engine v6 dynamic wave (6.0.0a4.dev1)

Hydra
Hydra 17 (NEER AI, Rust): its urban-drainage engine on the SWMM data model, run through its CLI with default settings
#9= 167 % off

Rate the error shrinks on finer grids: 0.039 (90 % range -0.7 to 0.77); the method's expected rate is 0.8 or more

Run time, finest grid: 1.3 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
• 49 cm off
76 % of the exact profile's mean depth, 0.640 m
Average flow error
• 2.55 m²/s off
167 % of the 1.53 m²/s unit discharge
Error by grid (L1 h)
· 0.2 m: 0.512 · 0.1 m: 0.434 · 0.05 m: 0.486
reported, not counted · the checks above are scored on the 0.05 m grid
Improves with finer grids
· rate 0.04 (90 % range −0.70 to 0.77)
reported, not counted · the scheme's design order is 1

Scored with method 3.0 · Score card: Hydra urban drainage (17.0.0/4.1.1)

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
#11= 189 % off

Rate the error shrinks on finer grids: -0.17 (90 % range -2.7 to 2.4); the method's expected rate is 0.8 or more

Run time, finest grid: 1.3 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
• 56 cm off
88 % of the exact profile's mean depth, 0.640 m
Average flow error
• 2.89 m²/s off
189 % of the 1.53 m²/s unit discharge
Error by grid (L1 h)
· 0.2 m: 0.446 · 0.1 m: 0.308 · 0.05 m: 0.563
reported, not counted · the checks above are scored on the 0.05 m grid
Improves with finer grids
· rate −0.17 (90 % range −2.73 to 2.40)
reported, not counted · the scheme's design order is 1

Scored with method 3.0 · Score card: EPA SWMM 5.1.15

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
#11= 189 % off

Rate the error shrinks on finer grids: -0.17 (90 % range -2.7 to 2.4); the method's expected rate is 0.8 or more

Run time, finest grid: 1.3 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
• 56 cm off
88 % of the exact profile's mean depth, 0.640 m
Average flow error
• 2.89 m²/s off
189 % of the 1.53 m²/s unit discharge
Error by grid (L1 h)
· 0.2 m: 0.446 · 0.1 m: 0.308 · 0.05 m: 0.563
reported, not counted · the checks above are scored on the 0.05 m grid
Improves with finer grids
· rate −0.17 (90 % range −2.73 to 2.40)
reported, not counted · the scheme's design order is 1

Scored with method 3.0 · Score card: EPA SWMM 5.2.4

Not run yet: HEC-RAS 7.0, GeoClaw, TUFLOW, MIKE 21, Iber, BASEMENT, Delft3D FM
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Error shrinks as the grid gets finer

Average error on each grid. A steeper line means the model converges faster.

0.03 mm0.1 mm0.3 mm1 mm3 mm1 cm3 cm10 cm30 cm0.050.050.10.10.10.20.20.2grid cell sizeTELEMAC-2D openTELEMAC 9.1: rate 0.94ANUGA 4.0.1: rate 0.91LISFLOOD-FP 8.3 · FV1: rate 0.95LISFLOOD-FP 8.3 · DG2: rate 0.93LISFLOOD-FP 8.3 · ACC: rate -0.12EPA SWMM 5.2.4 dynamic wave: rate -0.17OpenSWMM 6 dynamic wave: rate -0.27OpenSWMM 6 finite volume: rate 1Hydra urban drainage: rate 0.039SWMM 5.1.15 previous release: rate -0.17Basilisk Saint-Venant: rate 2Landlab OverlandFlow: rate 0.042
TELEMAC-2D · rate 0.94ANUGA · rate 0.91LISFLOOD-FP FV1 · rate 0.95LISFLOOD-FP DG2 · rate 0.93LISFLOOD-FP ACC · rate -0.12EPA SWMM 5.2.4 · rate -0.17OpenSWMM 6 · rate -0.27OpenSWMM 6 · rate 1Hydra · rate 0.039SWMM 5.1.15 · rate -0.17Basilisk · rate 2Landlab · rate 0.042

Status of this test

Candidate. To become frozen it needs: maintainer review recorded.

Technical details for reviewers Checks, reference, inputs, sources

Checks and why each limit was chosen

CheckDifference measured as a percentage ofLatestDifferenceWhy this check
L1_h
L1 of h · in the score
of the exact profile's mean depth, 0.640 m–Average depth error under 5 mm (1 % of the downstream depth) once steady; the critical point at the crest is where schemes struggle.
L1_Q
L1 of Q · in the score
of the 1.53 m²/s unit discharge–Discharge within 1 % of q on average.
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.swashes.steady_bump.

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.

  • ✓Data licence verifiedfor candidateanalytic-public
  • ✓All inputs availablefor candidateall committed or fetched by SHA-256
  • ✓Reference (truth) availablefor candidateanalytic generator
  • ✓Every tolerance justifiedfor candidateeach gating criterion has a rationale
  • ✓A published run passesfor frozen6 passing score card(s)
  • ✓Order of accuracy shownfor frozenobserved order meets the minimum
  • ✓Two independent codes passfor frozenpassing codes: ANUGA 4.0.1, Basilisk Saint-Venant, LISFLOOD-FP 8.3 DG2, LISFLOOD-FP 8.3 FV1, OpenSWMM Engine v6 finite volume, openTELEMAC-2D v9.1.1
  • ✗Maintainer review recordedfor frozenno maintainer review recorded

Inputs

FileRoleFormatSHA-256Get it
inputs/params.jsonparametersjson7b858a1d063d…Download

About this test

Physics

The same channel and bump with \(q = 1.53\) m²/s. The flow is critical at the crest (\(h_c = (q^2/g)^{1/3}\), head \(1.5 h_c + 0.2\)), subcritical upstream and supercritical downstream, with no jump. As in SWASHES, 0.66 m is held downstream only while the outflow is subcritical: once the flow leaving the channel is supercritical it needs no downstream condition. Each depth is the subcritical (upstream of the crest) or supercritical root of the Bernoulli cubic.

What it checks

The switch through critical flow at a control section, where many schemes produce a glitch or settle on the wrong branch.

Citation

Delestre et al. (2013), SWASHES, doi:10.1002/fld.3741.

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-041_swashes_bump_transcritical · version 1.0.0 · data licence analytic-public