Source : Analytical solution (Joukowsky) and independently written reference MOC (verification/cvb/run_cvb.js, cases CV-001 and CV-002)
When a valve closes at once, the pressure rise equals a·V₀/g and lasts 2L/a. Does CBELIER reproduce both values, and the whole curve of a separately written reference computation?
A reservoir feeds a 600 m pipe closed abruptly by a valve at t = 0.5 s. The initial velocity is small (0.10 m/s) so that friction, which CBELIER cannot switch off, stays negligible. The head at the valve is compared with the Joukowsky formula and with a frictionless method-of-characteristics computation written independently of the engine.
| Data | Value | Status |
|---|---|---|
| Pipe: length, diameter | 600 m; 0.50 m | DEFINED |
| Wave speed a | 1,200 m/s | DEFINED |
| Upstream reservoir; downstream of the valve | 150 m; 100 m | DEFINED |
| Initial velocity V₀ (small: friction negligible) | 0.10 m/s | DEFINED |
| Mesh: 20 reaches, Courant number = 1 | 20 | DEFINED |
| Reference: separately written frictionless MOC (same scheme) | — | DEFINED |
| Indicator | CBELIER | Reference | Difference |
|---|---|---|---|
| Pressure rise ΔH (V₀ = 0.10 m/s) | 12.24 m | 12.23 m | 0.1 % |
| Plateau duration (2L/a = 1.00 s) | 0.975 s | 1.000 s | 1 time step |
| RMS difference to the reference curve | 2.00 % ΔH | — | tolerance 2 % |
| Suite check (higher velocity) | 102.31 m | 101.63 m | 0.7 % |
The pressure rise and the plateau duration are reproduced; the 2 % RMS difference comes from the steep fronts, where a one-step shift is enough. At a higher velocity the difference to Joukowsky rises to 0.7 %: this is the expected effect of friction.