Exact answer known1D · pressurizedCandidate

Water hammer: valve slammed shut

Is the pressure surge right when a valve shuts instantly?

Test A1P-020
Joukowsky (1900)
Version 3.0.0

Time since the start

Press play, or drag the slider, to watch the exact answer unfold. Models are compared at the end, t = 0.5 s.

What happens

Water moving at speed is stopped dead by a valve. The pressure jumps by the Joukowsky amount and the surge races back up the pipe at the speed of sound in water.

Why it matters

Surges burst pipes and damage pumps. Surge protection is sized from exactly this number.

A good model must

get the peak pressure within 2 %
store exactly the water that kept flowing in
converge at least at the rate a sharp front allows

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 20 m down to 2.5 m cells; the checks are scored on the 2.5 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	Demo 1D suite example	<0.01 %	Peak pressure	<0.01 %	–
2	TSNet water hammer · MOC	0.13 %	Peak pressure	0.13 %	–

Demo 1D

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

#1 under 0.01 % off

Rate the error shrinks on finer grids: 0.49 (90 % range 0.48 to 0.5); the method's expected rate is 0.4 or more

Peak pressure

• < 0.0001 % off

Water stored by compression

· < 0.0001 % error

conservation, reported beside the score

Error by grid (L1 p)

· 20 m: 55,037 · 10 m: 39,401 · 5 m: 28,034 · 2.5 m: 19,885

reported, not counted · the checks above are scored on the 2.5 m grid

Improves with finer grids

· rate 0.49 (90 % range 0.48 to 0.50)

reported, not counted · the scheme's design order is 0.5

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.

The test itself (inputs, exact answer, checks): A1P-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.

TSNet

TSNet 0.3.1 (Xing and Sela 2020), an open-source water-hammer solver: the method of characteristics on an EPANET network

#2 0.13 % off

Rate the error shrinks on finer grids: 1.9 (90 % range 0.36 to 3.4); the method's expected rate is 0.4 or more

Settings: tsnet (method of characteristics on a WNTR network; the pipe split into reaches of the grid length)

Peak pressure

• 0.13 % off

Water stored by compression

· 0.13 % error

conservation, reported beside the score

Error by grid (L1 p)

· 20 m: 20,251 · 10 m: 10,551 · 5 m: 653 · 2.5 m: 654

reported, not counted · the checks above are scored on the 2.5 m grid

Improves with finer grids

· rate 1.89 (90 % range 0.36 to 3.41)

reported, not counted · the scheme's design order is 0.5

Scored with method 3.0 · Score card: TSNet 0.3.1

Run it yourself

TSNet 0.3.1 · runs on Linux · produced by scripts/run_tsnet.py in track-a.yml.

git clone https://github.com/scott-jeffers/benchmark1d2d && cd benchmark1d2d
git checkout 71dc10fc07a9
python -m pip install -e ".[dev]"
python3 -m venv .venv-tsnet && .venv-tsnet/bin/python -m pip install "numpy<2" "tsnet==0.3.1"
python scripts/run_tsnet.py --tsnet-python .venv-tsnet/bin/python

The model files the suite wrote for this run (.zip, 1.1 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, TELEMAC-2D, ANUGA, 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 0.49TSNet · rate 2

Status of this test

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

Download inputs (.zip)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
peak_pressure peak_error of p · in the score	already a percentage	–	Peak pressure within ±2% of Joukowsky rise Δp = ρ a V0.
storage_balance storage_balance_error of p · conservation, beside the score	already a percentage	–	Mass balance with no free parameter: until the first reflection the reservoir keeps delivering V0 while the valve is shut, and the pipe must store exactly that volume by compression, so ∫Δp dx = ρa²V0t. A conservative scheme meets it to round-off; 1 % allows non-conservative interpolation schemes that are otherwise accurate.
convergence observed order of L1 error in p · reported, not counted	the design order, 0.5	–	Measured from the error on every refinement level, as in ASME V&V 20.

Reference

Exact solution from references.joukowsky.pressure_wave.

More figures

Exact, t = 0.1 s
Exact, t = 0.25 s
Exact, t = 0.4 s
Exact, t = 0.5 s
Demo solver (MOC), t = 0.5 s

Joukowsky rise ρaV₀ = 1 MPa behind a sharp front; the fixed-grid solver smears the front.

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 frozen2 passing score card(s)
✓Order of accuracy shownfor frozenobserved order meets the minimum
✓Two independent codes passfor frozenpassing codes: TSNet 0.3.1, demo
✗Maintainer review recordedfor frozenno maintainer review recorded

Inputs

File	Role	Format	SHA-256	Get it
`inputs/params.json`	case_parameters	json	`1a1d580b46bc…`	Download

About this test

Physics

Frictionless pipe of length $L$ with reservoir at $x = 0$ and valve at $x = L$. Steady velocity $V_0$ toward the valve; instantaneous full closure at $t = 0$. Before the first upstream reflection ($0 \le t \le L/a$) the closed-end state propagates at celerity $a$ with pressure rise $\Delta p = \rho a V_0$. Default parameters: $L = a = 1000$, $V_0 = 1$, $\rho = 1000$ so $\Delta p = 10^6\,\mathrm{Pa}$ and first reflection at $t = 1\,\mathrm{s}$.

Mass balance

Until the first reflection the reservoir end still delivers $V_0$ while the valve is shut, and the pipe stores that inflow by compressing the water and stretching the wall. Per unit area the stored volume is $\int \Delta p \,dx / (\rho a^2)$, so

$$\int_0^L \Delta p\,dx = \rho a^2 V_0 t ,$$

whatever the front's shape. The storage_balance criterion checks this identity; it does not depend on how sharply a scheme resolves the front.

Case history

3.0.0 — the continuity criterion (mean $|u|$ behind the front) measured front smearing rather than mass, and failed accurate first-order schemes. It is replaced by the storage balance above. Scores are not comparable with 2.x.
2.0.0 — convergence target set from theory (0.5, minimum 0.4).

Citation

Joukowsky, N. (1900). "Über den hydraulischen Stoss in Wasserleitungsröhren." Mémoires de l'Académie Impériale des Sciences de St.-Pétersbourg, Series 8, 9(5). English translation: Simin, O. (1904). "Water hammer." Proc. Am. Water Works Assoc., 24, 341–424.

Analytic generator: references.joukowsky.pressure_wave.

Pitfalls

Score only before the first reflection; after $t > L/a$ the simple step-wave formula is invalid.
Numerical dispersion smears the pressure front; peak_error on $p$ is more robust than pointwise L∞ near the discontinuity.
Elastic wave speed $a$ must match the solver's pipe/fluid compressibility model; mismatched $a$ shifts both timing and $\Delta p$.
Instantaneous closure is an idealization — finite closure laws will under- predict the classic Joukowsky rise.

Sources

Joukowsky, N. (1900). Über den hydraulischen Stoss in Wasserleitungsröhren. Mem. Acad. Imp. Sci. St.-Petersbourg Ser.8 9(5).

Test A1P-020_joukowsky_instant_closure · version 3.0.0 · data licence analytic-public