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Product / TensorLynx / Mesh verification
Simulate · Mesh refinement and numerical verification
A single-mesh answer cannot tell you which of its digits are mesh noise, so a small design gain may be nothing at all. The TensorLynx platform builds a refinement ladder from one geometry, measures the observed order of accuracy, extrapolates with Richardson's method and reports the Grid Convergence Index against bars fixed before the first solve.
Bars fixed before the first solveAn untrustworthy GCI is withheld, not printedIterative error weighed against mesh error
The cost of the old way
Most engineering CFD and FEA numbers are still quoted from a single mesh. The ASME Journal of Fluids Engineering made the alternative a condition of publication: grid convergence must be established, iterative convergence addressed, and agreement with experiment alone does not justify a single-grid calculation. Design reviews rarely hold themselves to that bar, and the cost shows up late.
How TensorLynx does it
The coupled multiphysics chapter closes the balance at every interface. This one asks the next question: is the mesh fine enough for the number you are about to act on?
Every check is a declared rule with a cited reference: at least three systematically refined meshes, a refinement ratio of 1.3 or more, a fine-mesh GCI within 5 % to pass and 10 % for caution, with Roache's safety factor of 1.25. The bars are written before anything is measured and never moved after it. Method
At Send to Simulation you ask for ladder rungs. The geometry side meshes the same body at every level, one global size shrinking by the ladder ratio (1.5 by default), and records each rung in the hand-off. A sweep with no ladder says so and names the remedy instead of solving one mesh three times, and on the pipe-bend ladder a rung that would not refine every direction is refused before meshing. Method
The tail of each monitored quantity is fitted to separate noise from drift. The iterative uncertainty has to stay below a tenth of the discretisation uncertainty, Eça and Hoekstra's condition; otherwise the "mesh study" is partly measuring where each solve was stopped.
From the three values the platform solves the observed order p in Celik et al.'s form for unequal ratios, extrapolates to zero cell size with Richardson's method and computes the GCI on the finest mesh. On the published example it returns p 1.534, 6.1685 and a GCI of 2.175 % against the published 2.2 %. Measured · verification test
Verdicts read PASS, CAUTION, FAIL or UNKNOWN, and UNKNOWN is never a pass. A non-monotone triple has its GCI withheld with the reason. An order far from the scheme's formal order, or an asymptotic ratio outside 0.9–1.1, is written beside the number rather than buried in a log, and the study is recorded with its meshes.
Inside the engine
For the analyst who will be asked to defend the result. Each gate is a rule with a reference and a pass and caution bar; hover or focus a gate to read it.
h = (V / N)1/3r21 = h2/h1, r32 = h3/h2p = |ln|ε32/ε21| + q(p)| / ln r21φext = φ1 + (φ1 − φ2) / (r21p − 1)GCIfine = Fs |e21| / (r21p − 1), Fs = 1.25GCI32 / (r21p GCI21) ≈ 1The order equation, with q(p) correcting for unequal ratios, is solved by fixed-point iteration; the three-mesh layout and safety factors follow Roache and NASA's NPARC guidance. Node and cell counts are never treated as converging quantities. One candid detail: on exactly three meshes the asymptotic ratio is computed from the same values that fitted p, so it cannot fail; over 400 synthetic power-law triples it landed between 0.89 and 0.99 every time. Synthetic It is read with the order, and becomes an independent test from four meshes.
φ(k) ≈ a + b·k over the last 100 iterationsuiter = 2 · max(noise, |b| · window)uiter / |φ| ≤ 0.1 % pass, ≤ 1 % cautionuiter / uh ≤ 0.10 pass, ≤ 0.33 cautionA residual drop of five orders passes and three reads caution, and the rule says openly that this is a convention. What matters is whether the band is smaller than the design change being chased, and that comparison is a gate of its own.
unum = √(uh2 + uiter2)E = S − Duval = √(unum2 + uD2)Following ASME V&V 20, when |E| exceeds uval a real modelling error is resolved and worth chasing; when it does not, numerical error must come down before a smaller discrepancy can be seen. References are kept in a registry with their own uncertainty, conditions, citation and licence. Structural work follows the same split, as in ASME V&V 10 and NAFEMS guidance.
Solution verification means little if the solver path is wrong. The structural and thermal path runs a ladder of closed-form and manufactured-solution cases, each against a bar declared first: Measured
cantilever 0.44 %, Kirsch plate 0.17 %, Lamé bore 0.030 %clamped and free-free ≤ 0.30 %L2 order 3.06, formal 3time order 0.99, formal 1Solver adapters are checked by a seven-level conformance kit that names a remedy for each failure.
Evidence you can check
Every value below comes from recorded runs through the product path, measured against bars declared beforehand. The most convincing result is the one where the estimator said no.
Celik et al.'s worked example returns p 1.534 (published 1.53), φext 6.1685 (published 6.1685) and GCI 2.175 % (published 2.2 %). Non-monotone triples are rejected, not reported.
815 → 2,126 → 6,819 cells. Tip displacement: p 2.770, GCI 0.074 %, ratio 1.0011, converged. Peak von Mises stress: p 0.507, GCI 15.04 %, ratio 0.692, flagged, because stress at a fully fixed re-entrant edge is singular. Modelled in Geometry, three rungs at Send to Simulation, Run sweep on the Design study page, band read off the screen.
Stress aggregate 23.63, 24.40, 24.57 MPa on 1,635, 3,615 and 9,833 cells: GCI 0.13 %. The optimised design moved it 24.4 → 9.50 MPa (−61.1 %) at constant volume, and −59.0 % again on the fine mesh. At the selected design the medium and fine meshes differ by 6.0 %, and that goes into the error budget.
Peak temperature changed by −0.043 % against a GCI of 0.00015 %. A small gain is a real gain when the band is smaller still, and the platform shows both.
Each rung multiplies the cell count. Memory is predicted from cell count, measured on flow meshes of 703,705 and 1,369,436 cells, and a run the machine cannot hold is refused before it starts, with its remedy.
What it changes for your programme
Every delta in a design review arrives with its numerical band, so "better" means resolved, not lucky. Gradients for adjoint optimisation are only worth following when the change they promise is larger than that band.
Three meshes from one geometry, the order solved, the warnings beside the number. The afternoon of spreadsheets becomes a sweep you can repeat for the design that ships, then re-solve in high-fidelity reassessment.
Verification evidence in the vocabulary reviewers already use: GCI, observed order, comparison error, validation uncertainty. It sits with the run's provenance record, not in someone's inbox.
Intake pressure recovery or drag deltas between candidates, each checked against the band before it enters a trade study.
Duct and cooling pressure losses where the gain is a few per cent and the mesh noise must be shown to be smaller.
Thermal resistance of heat-exchanger and cold-plate variants, with iterative settling proved before the grid study starts.
Brackets and mounts where peak stress at sharp corners will not converge, so an aggregate or a stress at a distance is verified instead.
| Question | Typical workflow | With TensorLynx |
|---|---|---|
| Meshes | One mesh, judged by eye | A recorded ladder of three or more from one geometry |
| Order | Assumed second order | Observed p, compared with the formal order |
| Iterative error | Stopped at a residual target | Tail band, weighed against the mesh band |
| A bad study | A GCI printed anyway | Withheld or flagged, with the reason beside it |
| Design delta | Compared with nothing | Compared with its numerical band |
Simulation evidence supports engineering decisions; it does not replace required tests or sign-off. See the full loop on the TensorLynx overview.
FAQ
The Grid Convergence Index (GCI) is Roache's standard way of turning a systematic mesh refinement study into an error band on the fine-mesh value. TensorLynx solves the observed order of accuracy from three meshes, extrapolates to zero cell size with Richardson's method and applies a safety factor of 1.25. On the published Celik et al. worked example it returns an observed order of 1.534 and a GCI of 2.175 %, against the published 1.53 and 2.2 %.
At least three, systematically refined from the same geometry, so the order is measured rather than assumed. A refinement ratio of 1.3 or more passes and 1.1 to 1.3 reads caution, because closer meshes let iterative and round-off error swamp the difference. With only two meshes a GCI needs an assumed order and a safety factor of 3.
No. Verification asks whether the equations are solved accurately; validation asks whether they are the right equations for the physics. TensorLynx keeps them apart in the ASME V&V 20 sense: discretisation and iterative uncertainty combine into a numerical uncertainty, and only then is the comparison error against a reference judged against the validation uncertainty. A converged mesh does not make a model right, and no simulation replaces required tests or sign-off.
It is reported as such, beside the number. A non-monotone mesh triple has its GCI withheld with the reason; an observed order far from the scheme's formal order, or an asymptotic ratio outside 0.9 to 1.1, appears as a warning next to the value. On a recorded cantilever study the peak stress at the fixed edge, singular in the continuum, was flagged exactly this way while the tip displacement passed.
Not automatically, and TensorLynx does not assume it. On the recorded bracket family the nominal design's GCI was 0.13 %, while at the selected design the medium and fine meshes differed by 6.0 %. The improvement of 59 to 61 % was far larger than both, and the per-design difference went into the error budget rather than being assumed away.
Before the mesh study. Each rung's monitored quantity is checked for settling, its remaining drift is estimated from the tail of the history, and the iterative uncertainty must stay below a tenth of the discretisation uncertainty to pass. Otherwise the differences between meshes partly measure where each solve was stopped.
Yes. OLTRION engineers set up the refinement ladder on your geometry, run the iterative and grid checks against bars agreed with you before the first solve, and hand over the numbers with their bands and warnings, so your team can repeat the study and defend it in review.
Every capability hands its result to the next on the same model, the same units and the same record: geometry feeds physics, physics feeds sensitivities and learning, optimisation proposes, verification confirms, and the history keeps every step reproducible.
TensorLynx is built and run by the engineers who use it on client work. You can start small, with one geometry and one question, and grow into a workflow your own team owns.
Send a geometry, the objective and the constraints. We tell you which TensorLynx route answers it, what it needs from you, and what you will get back.
Our engineers run the loop on your problem: physics, sensitivities, optimisation and full-model verification, handed over with every setting on record.
A TensorLynx workflow, surrogate and verification gates set up around your product family, so the next design cycle starts where the last one ended.
Your team on TensorLynx, trained on your own cases, with OLTRION engineers behind it for the questions that need a specialist.
Simulation and AI predictions support engineering decisions; they do not replace the testing, approval and sign-off a product requires. Figures marked measured come from recorded TensorLynx runs on the stated case; figures marked synthetic or schematic illustrate a method.