GCI (Three-Mesh Method): Troubleshooting Guide
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My Gci 3mesh simulation is giving me unexpected results — convergence issues, maybe. How do I diagnose this systematically?
Gci 3mesh troubleshooting follows patterns once you know what to look for. Most issues fall into three buckets: convergence failures, accuracy problems, and result misinterpretation. Let me give you a systematic diagnostic framework rather than a list of random fixes.
That framing helps. Before we dive in — what's the single most common mistake engineers make with Gci 3mesh?
Honestly, it's skipping the sanity checks. Engineers set up a Gci 3mesh model, it converges, and they trust the result without verifying it against a hand calculation or a known benchmark. The solver gives you an answer regardless of whether your model is physically correct. Always run a simplified version first.
I computed the GCI from three meshes and got an observed order of 7.8 — clearly impossible — and a GCI of 0.01%. There's no way my solution is that accurate, right?
Right — that's not a good GCI result, it's a sign that the GCI's assumptions are broken. The Grid Convergence Index is only meaningful when the solution is in the asymptotic range and the observed order is near theory. An absurd observed order is a valuable alarm telling you those premises don't hold. This page walks through the troubles you meet in a three-mesh study, symptom by symptom.
Notation first. With coarse/medium/fine representative sizes \( h_3 > h_2 > h_1 \), solutions \( f_3, f_2, f_1 \), and refinement ratio \( r = h_{coarse}/h_{fine} \) (assumed constant), the observed order and fine-grid GCI are
$$ p = \frac{\ln\left|\dfrac{f_3 - f_2}{f_2 - f_1}\right|}{\ln r}, \qquad GCI_{fine} = \frac{F_s\,|e_a|}{r^p - 1}, \quad e_a = \frac{f_1 - f_2}{f_1} $$
with safety factor \( F_s = 1.25 \) for a systematic three-mesh study. Most troubles originate upstream of these formulas, in the data you feed them.
| Observed order | Meaning | Action |
|---|---|---|
| Within ~±0.5 of theory | Healthy; asymptotic range reached | Proceed to GCI |
| Below half of theory (p<1 for a 2nd-order scheme) | Pre-asymptotic, or local order loss (singularities, unresolved boundary layers) | Add finer levels; reconsider the quantity and location being evaluated |
| Far above theory (p>3–4) | Apparent superconvergence from error cancellation; GCI comes out unrealistically small | Clip p at the theoretical order and recompute GCI (conservative); check mesh-family systematicity |
| Negative / undefined (log of a negative) | Oscillatory convergence: \( (f_3-f_2) \) and \( (f_2-f_1) \) have opposite signs | See "oscillatory convergence" below — GCI is not valid as-is |
Classify the convergence type with the ratio \( R = (f_2 - f_1)/(f_3 - f_2) \): \( 0 < R < 1 \) monotonic, \( -1 < R < 0 \) oscillatory, \( |R| > 1 \) divergent. The GCI formula may be used only for monotonic convergence; for oscillatory behavior, report the oscillation band as the uncertainty (or extend to five meshes to confirm decay).
When results bounce up and down with refinement, check these causes in order:
Budget pressure tempts people toward \( r = 1.1 \), but a small ratio makes \( f_2 - f_1 \) tiny and buries it under round-off, iterative truncation, and convergence-tolerance jitter. Recommended: \( r \ge 1.3 \) (Roache's rule of thumb). In 3-D, element count scales roughly with \( r^3 \), so even \( r = 1.3 \) is only ~2.2× elements per level; if resources allow, uniform \( r = 2 \) gives the most interpretable series. For unstructured meshes, define the representative size from the cell count as \( h = (V/N)^{1/3} \) (2-D: \( (A/N)^{1/2} \)) and recompute the effective ratio — the mesher's nominal scaling factor frequently differs from it.
My displacement GCI is 0.5%, but the max-stress GCI is 12%. Which one do I report?
Both — that's the correct answer. GCI is a per-quantity index, not one number for the whole model. Integral-like quantities (displacements) converge fast; derivative, local quantities (stresses) converge slowly — that's normal behavior, not a defect. Report the GCI of every quantity used for design decisions. If the stress GCI is too large, build a locally refined series around that evaluation region. And if the stress point sits near a singularity (corner, point constraint), it will never mesh-converge — singularity classification comes before GCI.
Once monotonic convergence is confirmed, adding the Richardson extrapolate and a consistency check makes the report much stronger:
$$ f_{ext} = f_1 + \frac{f_1 - f_2}{r^p - 1} $$
The consistency check asks whether \( GCI_{23} \approx r^p \, GCI_{12} \). A large mismatch means the series has not reached the asymptotic range — add one finer level. Organized in a table, the numbers stand up to audit:
| Check | Pass criterion | If it fails |
|---|---|---|
| Convergence type (ratio R) | 0 < R < 1 (monotonic) | Oscillatory → report band; divergent → rebuild the series |
| Observed order p | Theory ±0.5 | Clip or add levels; inspect boundaries/singularities |
| Effective ratio r | r ≥ 1.3 | Space the levels further apart |
| Asymptotic-range check | GCI23 / (r^p·GCI12) ≈ 1 (0.9–1.1) | Add a finer level |
| Iterative residuals | ≥2 orders below discretization error | Tighten and re-run |
For the full procedure and worked examples see the consolidated GCI (three-mesh method) guide; neighboring topics: h-refinement fundamentals and troubleshooting MMS convergence rates.