Exact answer known1D · free surfaceCandidate

Standing hydraulic jump

Does the model hold a hydraulic jump in the right place, at the right height?

Test A1F-020
Bélanger (1828)
Version 1.0.0

Hidden at first because they are far off the exact answer: EPA SWMM 5.2.4, OpenSWMM 6 dynamic wave, OpenSWMM 6 finite volume, Hydra, SWMM 5.1.15. Click a name to show it.

What happens

Fast, shallow water (20 cm deep) meets slow, deep water (61 cm) and jumps abruptly between the two. With these exact depths the jump stands still at 50 m.

Why it matters

Jumps form below weirs, spillways and culverts, where they decide scour and the size of energy dissipators. A jump that drifts means the wrong design.

A good model must

match the depth profile within 1 %
keep the jump where it should be (no drift)
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 2 m down to 0.25 m cells; the checks are scored on the 0.25 m grid, and each card lists the error on every grid. Compare them in the results viewer →

Rank	Model	Difference	Largest difference in	Mass error	Run time
1	TELEMAC-2D openTELEMAC 9.1	0.049 %	Depth profile	0.046 %	23.1 s
2	Basilisk Saint-Venant	0.093 %	Depth profile	0.052 %	0.29 s
3	Demo 1D suite example	0.15 %	Depth profile	0.061 %	–
4	ANUGA 4.0.1	0.28 %	Depth profile	0.28 %	27.6 s
5	OpenSWMM 6 finite volume	50 %	Depth profile	48 %	3.3 s
6	Hydra urban drainage	71 %	Depth profile	13 %	25.1 s
7=	OpenSWMM 6 dynamic wave	99 %	Depth profile	34 %	6.9 s
7=	SWMM 5.1.15 previous release	102 %	Depth profile	29 %	6.3 s
7=	EPA SWMM 5.2.4 dynamic wave	102 %	Depth profile	29 %	6.4 s

TELEMAC-2D

openTELEMAC-2D 9.1.1, run with its default finite-volume settings

#1 0.049 % off

Rate the error shrinks on finer grids: 0.95 (90 % range 0.86 to 1); the method's expected rate is 0.8 or more

Run time, finest grid: 23.1 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); HLLC scheme (the default kinetic scheme is unstable here)

Depth profile

• 0.049 % off

Jump stays put

· 0.046 % error

conservation, reported beside the score

Error by grid (L1 h)

· 2 m: 0.00142 · 1 m: 0.0008 · 0.5 m: 0.0004 · 0.25 m: 0.0002

reported, not counted · the checks above are scored on the 0.25 m grid

Improves with finer grids

· rate 0.95 (90 % range 0.86 to 1.04)

reported, not counted · the scheme's design order is 1

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

Run it yourself

openTELEMAC-2D v9.1.1 · runs on Linux · produced by scripts/run_telemac.py in track-a.yml.

git clone https://github.com/scott-jeffers/benchmark1d2d && cd benchmark1d2d
git checkout 71dc10fc07a9
python -m pip install -e ".[dev]"
conda create -n telemac -c conda-forge opentelemac=v9.1.1 python=3.12
python scripts/run_telemac.py --telemac-prefix "$(conda info --base)/envs/telemac" A1F-020

The model files the suite wrote for this run (.zip, 41 KB): the exact inputs the solver read (one folder per grid, where the test has several), with their SHA-256.

The test itself (inputs, exact answer, checks): A1F-020.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.

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)

#2 0.093 % off

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

Run time, finest grid: 0.29 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)

Depth profile

• 0.093 % off

Jump stays put

· 0.052 % error

conservation, reported beside the score

Error by grid (L1 h)

· 2 m: 0.00304 · 1 m: 0.00152 · 0.5 m: 0.000759 · 0.25 m: 0.000379

reported, not counted · the checks above are scored on the 0.25 m grid

Improves with finer grids

· rate 1.00 (90 % range 1.00 to 1.00)

reported, not counted · the scheme's design order is 1

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

Run it yourself

Basilisk Saint-Venant (snapshot de851a91) · runs on Linux · produced by scripts/run_basilisk.py in open-solvers.yml.

git clone https://github.com/scott-jeffers/benchmark1d2d && cd benchmark1d2d
git checkout 71dc10fc07a9
python -m pip install -e ".[dev]"
curl -O https://basilisk.fr/basilisk/basilisk.tar.gz && tar xzf basilisk.tar.gz  # a rolling snapshot: the score card names its SHA-256
(cd basilisk/src && ln -s config.gcc config && make -k; make)
python scripts/run_basilisk.py --basilisk basilisk/src A1F-020

The model files the suite wrote for this run (.zip, 0.58 KB): the exact inputs the solver read (one folder per grid, where the test has several), with their SHA-256.

The script writes a small Basilisk C program for the test (kept in the model files below) and compiles it with qcc.

Demo 1D

Worked example that ships with the suite: plain, well-understood schemes

#3 0.15 % off

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

Depth profile

• 0.15 % off

Jump stays put

· 0.061 % error

conservation, reported beside the score

Error by grid (L1 h)

· 2 m: 0.00486 · 1 m: 0.00243 · 0.5 m: 0.00122 · 0.25 m: 0.000607

reported, not counted · the checks above are scored on the 0.25 m grid

Improves with finer grids

· rate 1.00 (90 % range 1.00 to 1.00)

reported, not counted · the scheme's design order is 1

Scored with method 3.0 · Score card: demo

Run it yourself

demo · version 0.1.0 · runs on any · produced by scripts/run_vertical_slice.py in track-a.yml.

git clone https://github.com/scott-jeffers/benchmark1d2d && cd benchmark1d2d
git checkout 71dc10fc07a9
python -m pip install -e ".[dev,engines]"
python scripts/run_vertical_slice.py

The model files for this run will be published with its next run.

ANUGA

ANUGA 4.0.1 (Geoscience Australia / ANU), default settings on a triangular mesh

#4 0.28 % off

Rate the error shrinks on finer grids: -0.016 (90 % range -0.57 to 0.54); the method's expected rate is 0.8 or more

Run time, finest grid: 27.6 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)

Depth profile

• 0.28 % off

Jump stays put

· 0.28 % error

conservation, reported beside the score

Error by grid (L1 h)

· 2 m: 0.000956 · 1 m: 0.00169 · 0.5 m: 0.00117 · 0.25 m: 0.00112

reported, not counted · the checks above are scored on the 0.25 m grid

Improves with finer grids

· rate −0.02 (90 % range −0.57 to 0.54)

reported, not counted · the scheme's design order is 1

Scored with method 3.0 · Score card: ANUGA 4.0.1

Run it yourself

ANUGA 4.0.1 · runs on Linux · produced by scripts/run_anuga.py in open-solvers.yml.

git clone https://github.com/scott-jeffers/benchmark1d2d && cd benchmark1d2d
git checkout 71dc10fc07a9
conda create -n anuga -c conda-forge anuga=4.0.1 python=3.12 pip scipy
conda activate anuga
python -m pip install -e ".[dev]"
python scripts/run_anuga.py A1F-020

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.

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

#5 50 % off

Rate the error shrinks on finer grids: -0.0083 (90 % range -0.016 to -0.00071); the method's expected rate is 0.8 or more

Run time, finest grid: 3.3 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)

Depth profile

• 50 % off

Jump stays put

· 48 % error

conservation, reported beside the score

Error by grid (L1 h)

· 2 m: 0.201 · 1 m: 0.203 · 0.5 m: 0.204 · 0.25 m: 0.204

reported, not counted · the checks above are scored on the 0.25 m grid

Improves with finer grids

· rate −0.01 (90 % range −0.02 to −0.00)

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)

Run it yourself

OpenSWMM Engine v6 finite volume (6.0.0a4.dev1) · runs on Linux · produced by scripts/run_swmm_track_a.py in track-a.yml.

git clone https://github.com/scott-jeffers/benchmark1d2d && cd benchmark1d2d
git checkout 71dc10fc07a9
python -m pip install -e ".[dev,engines]"
python -m venv .venv-openswmm
.venv-openswmm/bin/python -m pip install "openswmm==6.0.0a4.dev1" numpy
python scripts/run_swmm_track_a.py A1F-020 --engines openswmm-fv --openswmm-python .venv-openswmm/bin/python

The model files the suite wrote for this run (.zip, 16 KB): the exact inputs the solver read (one folder per grid, where the test has several), with their SHA-256.

Hydra

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

#6 71 % off

Rate the error shrinks on finer grids: 0.25 (90 % range -0.13 to 0.63); the method's expected rate is 0.8 or more

Run time, finest grid: 25.1 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 (DYNWAVE routing, conduit per grid cell)

Depth profile

• 71 % off

Jump stays put

· 13 % error

conservation, reported beside the score

Error by grid (L1 h)

· 2 m: 0.44 · 1 m: 0.388 · 0.5 m: 0.238 · 0.25 m: 0.29

reported, not counted · the checks above are scored on the 0.25 m grid

Improves with finer grids

· rate 0.25 (90 % range −0.13 to 0.63)

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)

Run it yourself

Hydra urban drainage (17.0.0/4.1.1) · runs on Linux · produced by scripts/run_swmm_track_a.py in track-a.yml.

git clone https://github.com/scott-jeffers/benchmark1d2d && cd benchmark1d2d
git checkout 71dc10fc07a9
python -m pip install -e ".[dev,engines]"
HYDRA=$(python scripts/fetch_hydra.py .hydra)  # the pinned Hydra 17 CLI
python scripts/run_swmm_track_a.py A1F-020 --engines hydra-uds --hydra-exe "$HYDRA"

The model files the suite wrote for this run (.zip, 16 KB): the exact inputs the solver read (one folder per grid, where the test has several), with their SHA-256.

OpenSWMM 6

OpenSWMM Engine v6 (HydroCouple's SWMM 6, pre-release) with dynamic-wave routing

#7= 99 % off

Rate the error shrinks on finer grids: 0.11 (90 % range -0.063 to 0.28); the method's expected rate is 0.8 or more

Run time, finest grid: 6.9 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)

Depth profile

• 99 % off

Jump stays put

· 34 % error

conservation, reported beside the score

Error by grid (L1 h)

· 2 m: 0.491 · 1 m: 0.538 · 0.5 m: 0.463 · 0.25 m: 0.402

reported, not counted · the checks above are scored on the 0.25 m grid

Improves with finer grids

· rate 0.11 (90 % range −0.06 to 0.28)

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)

Run it yourself

OpenSWMM Engine v6 dynamic wave (6.0.0a4.dev1) · runs on Linux · produced by scripts/run_swmm_track_a.py in track-a.yml.

git clone https://github.com/scott-jeffers/benchmark1d2d && cd benchmark1d2d
git checkout 71dc10fc07a9
python -m pip install -e ".[dev,engines]"
python -m venv .venv-openswmm
.venv-openswmm/bin/python -m pip install "openswmm==6.0.0a4.dev1" numpy
python scripts/run_swmm_track_a.py A1F-020 --engines openswmm-dw --openswmm-python .venv-openswmm/bin/python

The model files the suite wrote for this run (.zip, 16 KB): the exact inputs the solver read (one folder per grid, where the test has several), with their SHA-256.

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

#7= 102 % off

Rate the error shrinks on finer grids: 0.13 (90 % range -0.17 to 0.43); the method's expected rate is 0.8 or more

Run time, finest grid: 6.3 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 (DYNWAVE routing, conduit per grid cell)

Depth profile

• 102 % off

Jump stays put

· 29 % error

conservation, reported beside the score

Error by grid (L1 h)

· 2 m: 0.491 · 1 m: 0.538 · 0.5 m: 0.363 · 0.25 m: 0.414

reported, not counted · the checks above are scored on the 0.25 m grid

Improves with finer grids

· rate 0.13 (90 % range −0.17 to 0.43)

reported, not counted · the scheme's design order is 1

Scored with method 3.0 · Score card: EPA SWMM 5.1.15

Run it yourself

EPA SWMM 5.1.15 · version data5.1.15 · runs on Linux · produced by scripts/run_swmm_track_a.py in track-a.yml.

git clone https://github.com/scott-jeffers/benchmark1d2d && cd benchmark1d2d
git checkout 71dc10fc07a9
python -m pip install -e ".[dev,engines]"
python3.10 -m venv .venv-swmm51 && .venv-swmm51/bin/python -m pip install "swmm-toolkit==0.10.0"  # EPA SWMM 5.1.15
python scripts/run_swmm_track_a.py A1F-020 --engines swmm515 --swmm51-python .venv-swmm51/bin/python

The model files the suite wrote for this run (.zip, 16 KB): the exact inputs the solver read (one folder per grid, where the test has several), with their SHA-256.

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

#7= 102 % off

Rate the error shrinks on finer grids: 0.13 (90 % range -0.17 to 0.43); 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)

Depth profile

• 102 % off

Jump stays put

· 29 % error

conservation, reported beside the score

Error by grid (L1 h)

· 2 m: 0.491 · 1 m: 0.538 · 0.5 m: 0.363 · 0.25 m: 0.414

reported, not counted · the checks above are scored on the 0.25 m grid

Improves with finer grids

· rate 0.13 (90 % range −0.17 to 0.43)

reported, not counted · the scheme's design order is 1

Scored with method 3.0 · Score card: EPA SWMM 5.2.4

Run it yourself

EPA SWMM 5.2.4 · runs on Linux · produced by scripts/run_swmm_track_a.py in track-a.yml.

git clone https://github.com/scott-jeffers/benchmark1d2d && cd benchmark1d2d
git checkout 71dc10fc07a9
python -m pip install -e ".[dev,engines]"
python scripts/run_swmm_track_a.py A1F-020 --engines swmm524

The model files the suite wrote for this run (.zip, 16 KB): the exact inputs the solver read (one folder per grid, where the test has several), with their SHA-256.

Not run yet: HEC-RAS 7.0, GeoClaw, LISFLOOD-FP, TUFLOW, MIKE 21, Iber, BASEMENT, Delft3D FM

Run it and add yours →

Error shrinks as the grid gets finer

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

Demo 1D · rate 1TELEMAC-2D · rate 1ANUGA · rate 0.3EPA SWMM 5.2.4 · rate 0.19OpenSWMM 6 · rate 0.21OpenSWMM 6 · rate -0.0041Hydra · rate 0.21SWMM 5.1.15 · rate 0.19Basilisk · rate 1

Status of this test

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

Download inputs (.zip)Check your results in the browser Cite this test View on GitHub

Technical details for reviewers Checks, reference, inputs, sources

Checks and why each limit was chosen

Check	Difference measured as a percentage of	Latest	Why this check
jump_profile L1 of h · in the score	already a percentage	–	Depth profile within 1 % (relative L1) of the stationary Bélanger step at x = 50 m on the finest grid. A captured jump smeared over two cells contributes Δh·2dx/L ≈ 0.5 % at dx = 0.25 m; a drifting jump or wrong sequent depth exceeds it.
jump_stays_put global_mass_error of volume · conservation, beside the score	already a percentage	–	Stored volume within 0.1 % of the exact step: a jump that drifts by half a cell (0.125 m) on the finest grid changes the volume by 0.13 %, so this fails any solver that cannot hold the Rankine–Hugoniot balance.
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.belanger.sequent_depths.

More figures

Exact (stationary Bélanger jump)
Demo solver after 200 s

h₁ = 0.200 m, h₂ = 0.614 m, energy loss 0.145 m. The jump must stay at x = 50 m; the first-order scheme spreads it over about two cells.

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 frozen3 passing score card(s)
✓Order of accuracy shownfor frozenobserved order meets the minimum
✓Two independent codes passfor frozenpassing codes: Basilisk Saint-Venant, demo, openTELEMAC-2D v9.1.1
✗Maintainer review recordedfor frozenno maintainer review recorded

Inputs

File	Role	Format	SHA-256	Get it
`inputs/params.json`	case_parameters	json	`e9ccb8d3d60b…`	Download

About this test

Physics

On a horizontal frictionless bed, supercritical flow $h_1 = 0.2$ m, $Fr_1 = 2.5$ meets the sequent depth held downstream,

$$\frac{h_2}{h_1} = \tfrac12\left(\sqrt{1 + 8Fr_1^2} - 1\right) = 3.05 .$$

The jump conserves mass and momentum and dissipates energy. Started from the exact step at $x = 50$ m, it must stay there: on a frictionless bed its position is neutral, so any imbalance in the scheme shows up as drift.

What it checks

Shock capturing of a stationary jump: the conjugate depths, the Rankine–Hugoniot balance (no drift) and convergence of the captured profile at order 1 in L1, which is what any consistent shock-capturing scheme achieves. The demo first-order HLL solver holds the jump within one cell and converges at 1.00.

Case history

1.0.0 — grids 2, 1, 0.5, 0.25 m (the draft's 20 m grid had five cells in the channel); criteria on the relative L1 profile error and the stored volume.

Citation

Bélanger, J.-B. (1828). Essai sur la solution numérique de quelques problèmes relatifs au mouvement permanent des eaux courantes. Paris. Chow, V. T. (1959). Open-Channel Hydraulics, ch. 15. McGraw-Hill.

Sources

Bélanger, J. B. (1828). Essai sur la solution numérique de quelques problèmes relatifs au mouvement permanent des eaux courantes (Bélanger sequent-depth relation). Belanger-1828.

Test A1F-020_hydraulic_jump_belanger · version 1.0.0 · data licence analytic-public