Validation.

How close MeshWeave’s flow solves come to answers that are known. Each case is a synthetic part with a published result, solved exactly the way your part is: the same upload, the same solve, the same numbers back.

Quick solve: 7 of 7 points within tolerance, release v3.536, 2026-10-20. Full solve: 3 of 7 points within tolerance, release v3.523, 2026-10-19.

ResultsEvery case, both solves
casepointreferenceQuick solveFull solvetolerance, Quick / Full
Turbulent pipe frictionRe 10,000f = 0.03110.0301 −3.3 % within0.0371 +19.3 % outside±10 % / ±5 %
Re 20,000f = 0.02620.0253 −3.3 % within0.0291 +11.4 % outside±10 % / ±5 %
Re 50,000f = 0.02130.0203 −4.7 % within0.0220 +3.0 % within±10 % / ±5 %
Laminar pipe frictionRe 100f = 0.6400.611 −4.5 % within0.651 +1.8 % within±10 % / ±5 %
Re 200f = 0.3200.321 +0.2 % within0.326 +1.8 % within±10 % / ±5 %
Sudden expansion, area ratio 1:4Re 20,000K = 0.5630.596 +6.0 % withinrefused, no result±15 % / ±10 %
Sharp 90° mitre bend, square ductRe 20,000K = 1.201.07 −11.0 % withinno result±20 % / ±15 %

A point is within tolerance when the measured value is within the stated percentage of the reference. A refused solve is one the solver would not stand behind (it had not settled, or failed one of its own checks): it is shown as no result, never as a pass.

Turbulent pipe frictionDarcy friction factor f
0.0210k20k50kQuick solve, Re 10,000: f 0.0301 against 0.0311 (-3.3 %, tolerance ±10 %)Full solve, Re 10,000: f 0.0371 against 0.0311 (+19.3 %, tolerance ±5 %)Quick solve, Re 19,999: f 0.0253 against 0.0262 (-3.3 %, tolerance ±10 %)Full solve, Re 20,000: f 0.0291 against 0.0262 (+11.4 %, tolerance ±5 %)Quick solve, Re 49,998: f 0.0203 against 0.0213 (-4.7 %, tolerance ±10 %)Full solve, Re 50,000: f 0.0220 against 0.0213 (+3.0 %, tolerance ±5 %)Reynolds numberDarcy friction factor fQuick solveFull solvereference±10 % Quick, ±5 % Fulloutside tolerance

Quick solve: release v3.536, 2026-10-20. Full solve: release v3.523, 2026-10-19.

Reference. Colebrook–White equation (Colebrook 1939, J. Inst. Civil Engineers 11:133; Moody 1944, Trans. ASME 66:671), at the wall roughness the solves were given.

How it is measured. Two round tubes with a 12 mm bore, 20 and 40 diameters long, solved at the same flow. The friction factor comes from the difference in pressure loss between them, so what happens at the open ends cancels out, the way a lab measures it between two pressure taps.

240 × 18 × 18 mm, cut through the passage; filled dot the inlet, ring the outlet; solved on 0.857 mm cells.
480 × 18 × 18 mm, cut through the passage; filled dot the inlet, ring the outlet; solved on 0.857 mm cells.
Laminar pipe frictionDarcy friction factor f
0.20.51100200Quick solve, Re 100: f 0.611 against 0.640 (-4.5 %, tolerance ±10 %)Full solve, Re 100: f 0.651 against 0.640 (+1.8 %, tolerance ±5 %)Quick solve, Re 200: f 0.321 against 0.320 (+0.2 %, tolerance ±10 %)Full solve, Re 200: f 0.326 against 0.320 (+1.8 %, tolerance ±5 %)Reynolds numberDarcy friction factor fQuick solveFull solvereference±10 % Quick, ±5 % Fulloutside tolerance

Quick solve: release v3.536, 2026-10-20. Full solve: release v3.523, 2026-10-19.

Reference. Hagen–Poiseuille, f = 64/Re, exact for fully developed laminar flow in a round pipe.

How it is measured. The same two tubes at a slow, laminar flow. Exact theory applies here, so this case shows how close each solve comes to an answer that is known precisely.

240 × 18 × 18 mm, cut through the passage; filled dot the inlet, ring the outlet; solved on 0.857 mm cells.
480 × 18 × 18 mm, cut through the passage; filled dot the inlet, ring the outlet; solved on 0.857 mm cells.
Sudden expansion, area ratio 1:4loss coefficient on the upstream velocity head K
0.410.470.530.600.660.72QuickQuick solve, Re 20,002: K 0.596 against 0.563 (+6.0 %, tolerance ±15 %)Fullrefused, no resultloss coefficient KQuick solveFull solvereference±15 % Quick, ±10 % Fulloutside tolerance

Quick solve: release v3.536, 2026-10-20. Full solve: release v3.523, 2026-10-19.

Reference. Borda–Carnot, K = (1 − A₁/A₂)² = 0.5625, from a momentum balance across the step.

How it is measured. A square 8 mm duct opening suddenly into a 16 mm duct, and the 8 mm duct on its own at the same flow. The loss of the step is the difference, less the small friction of the wide section.

336 × 21 × 21 mm, cut through the passage; filled dot the inlet, ring the outlet; solved on 1 mm cells.
48 × 13 × 13 mm, cut through the passage; filled dot the inlet, ring the outlet; solved on 1 mm cells.
Sharp 90° mitre bend, square ductloss coefficient K
0.820.981.131.291.451.61QuickQuick solve, Re 20,003: K 1.068 against 1.200 (-11.0 %, tolerance ±20 %)Fullrefused, no resultloss coefficient KQuick solveFull solvereference±20 % Quick, ±15 % Fulloutside tolerance

Quick solve: release v3.536, 2026-10-20. Full solve: release v3.523, 2026-10-19.

Reference. Idelchik, Handbook of Hydraulic Resistance (3rd ed., 1996), sharp 90° elbow of square section, about 1.0–1.2 at this Reynolds number; held to 1.2.

How it is measured. A square 10 mm duct with a sharp right-angle turn, and a straight duct of the same centreline length at the same flow. The loss of the bend is the difference.

92 × 152 × 15 mm, cut through the passage; filled dot the inlet, ring the outlet; solved on 1 mm cells.
229 × 15 × 15 mm, cut through the passage; filled dot the inlet, ring the outlet; solved on 1 mm cells.
Not yetSaid plainly
Backward-facing step, reattachment length
Driver & Seegmiller (1985), AIAA J. 23:163
Not yet, on either solve. Reading where the flow reattaches needs a finer mesh along the shear layer behind the step than either solve builds today.
Lid-driven cavity, Re 100, 400 and 1000
Ghia, Ghia & Shin (1982), J. Comput. Phys. 48:387
Not yet: it needs a moving wall, which neither solve has.

Every case here is rerun on the server after a release that changes the flow solvers, and a point that slips holds the next release until it is fixed.