How do I install the Convergence Verification skill?

Run npx skillmds@latest add ashfordeou/convergence-verification in your terminal (requires Node.js), paste this page's agent-chat prompt into Claude, Cursor, or any MCP-connected agent, or download the SKILL.md file and copy it into your agent's skills directory.

Is Convergence Verification safe to use?

This skill has not completed SkillMD's automated safety review yet. SkillMD never runs a skill's scripts for you; review the SKILL.md before installing.

Which AI agents work with Convergence Verification?

This skill is tagged as working with Claude Code, Claude.ai, OpenAI Codex. SKILL.md is an open format, so most agents that read a skills directory can load it too.

Is Convergence Verification free to use?

Yes. Installing skills from SkillMD is free. This skill is licensed under Apache-2.

Who published Convergence Verification?

ashfordeOU (@ashfordeou) published this skill. Their other Agent Skills are listed on their SkillMD profile.

Convergence Verification by ashfordeou

Name: Convergence Verification
Author: ashfordeOU

Convergence Verification

Use when you must verify that a CFD or structural mesh sequence has converged: compute the observed order of accuracy from the finest, medium, and coarse solutions, apply Richardson extrapolation to estimate the exact solution, and report the grid convergence index (GCI) with the 1.25 safety factor. Produces the observed order, the extrapolated value, the GCI, and a monotone converged, oscillatory, or diverging verdict that gate whether the discretization error is acceptable for the assessment. Trigger: richardson extrapolation, grid convergence index, gci, observed order, refinement ratio, discretization error, mesh refinement study.

ashfordeOU 6b66881 3 files · 12.3 KB Updated Sep 17, 2026

File contents

Convergence Verification (cross-cutting/numerics/convergence-verification)

Use when the task is verifying that a CFD or structural mesh sequence has converged: computing the observed order of accuracy, Richardson extrapolation of the exact solution, and the grid convergence index (GCI) with its safety factor.

Domain quick reference

Three solutions from a systematic refinement family: f1 finest, f2 medium, f3 coarse, refinement ratio r = h_coarse / h_fine > 1.
Observed order p = ln((f3-f2)/(f2-f1)) / ln(r); valid only for a monotone sequence, ratio (f3-f2)/(f2-f1) > 0.
Richardson extrapolation f_exact = f1 + (f1 - f2) / (r**p - 1).
Grid convergence index gci = Fs * abs((f1 - f2) / f1) / (r**p - 1), safety factor Fs = 1.25 for three-grid studies.
Verdict from ratio (f3-f2)/(f2-f1): monotone converged when ratio

0, oscillatory when ratio < 0, diverging when abs(ratio) > 1 (diverging takes precedence on the negative branch).
f1, f2, f3 in any consistent solution units; r, p, and gci are dimensionless; gci is a fraction, not a percentage.

Workflow

Collect f1, f2, f3 from the three refinement levels and the constant refinement ratio r.
Compute the observed order with observed_order(f1, f2, f3, r).
Estimate the exact solution with richardson_extrapolation(f1, f2, r, p).
Bound the discretization error with grid_convergence_index(f1, f2, r, p, fs=1.25).
Classify the study with convergence_verdict(f1, f2, f3, r) and decide whether the finest mesh is adequate for the assessment.

Pitfalls

Calling the study converged on a non-monotone sequence: observed_order raises ValueError when the ratio (f3-f2)/(f2-f1) is not positive.
Using a refinement ratio r <= 1: the observed order is undefined; r must exceed 1.
Reporting the GCI as a percentage when the function returns a fraction.
Trusting the extrapolated value when the observed order is near zero: r**p - 1 collapses and the estimate is garbage.
Treating an oscillatory or diverging sequence as quantifiable: order, extrapolated value, and GCI are None when the sequence is not monotone.

Behavior contract (gate 3)

The grid convergence logic is exercised by the gate 3 contract test: scripts/test_convergence_verification.py against scripts/convergence_verification_logic.py (stdlib unittest, offline). Run: python3 scripts/test_convergence_verification.py

Compliance

NACA Report 824 is US government work (public domain); summary and physics values only, per standards-map.yaml. Convergence verification is generic numerical methodology: Richardson extrapolation and the GCI are standard discretization error estimation, not RTCA or SAE content.
compliance: STANDARDS-REF, gated: false.

---name: convergence-verificationdescription: Use when you must verify that a CFD or structural mesh sequence has converged: compute the observed order of accuracy from the finest, medium, and coarse solutions, apply Richardson extrapolation to estimate the exact solution, and report the grid convergence index (GCI) with the 1.25 safety factor. Produces the observed order, the extrapolated value, the GCI, and a monotone converged, oscillatory, or diverging verdict that gate whether the discretization error is acceptable for the assessment. Trigger: richardson extrapolation, grid convergence index, gci, observed order, refinement ratio, discretization error, mesh refinement study.license: Apache-2.0---# Convergence Verification (cross-cutting/numerics/convergence-verification)Use when the task is verifying that a CFD or structural meshsequence has converged: computing the observed order of accuracy,Richardson extrapolation of the exact solution, and the gridconvergence index (GCI) with its safety factor.## Domain quick reference- Three solutions from a systematic refinement family: f1 finest, f2 medium, f3 coarse, refinement ratio r = h_coarse / h_fine > 1.- Observed order p = ln((f3-f2)/(f2-f1)) / ln(r); valid only for a monotone sequence, ratio (f3-f2)/(f2-f1) > 0.- Richardson extrapolation f_exact = f1 + (f1 - f2) / (r**p - 1).- Grid convergence index gci = Fs * abs((f1 - f2) / f1) / (r**p - 1), safety factor Fs = 1.25 for three-grid studies.- Verdict from ratio (f3-f2)/(f2-f1): monotone converged when ratio > 0, oscillatory when ratio < 0, diverging when abs(ratio) > 1 (diverging takes precedence on the negative branch).- f1, f2, f3 in any consistent solution units; r, p, and gci are dimensionless; gci is a fraction, not a percentage.## Workflow1. Collect f1, f2, f3 from the three refinement levels and the constant refinement ratio r.2. Compute the observed order with observed_order(f1, f2, f3, r).3. Estimate the exact solution with richardson_extrapolation(f1, f2, r, p).4. Bound the discretization error with grid_convergence_index(f1, f2, r, p, fs=1.25).5. Classify the study with convergence_verdict(f1, f2, f3, r) and decide whether the finest mesh is adequate for the assessment.## Pitfalls- Calling the study converged on a non-monotone sequence: observed_order raises ValueError when the ratio (f3-f2)/(f2-f1) is not positive.- Using a refinement ratio r <= 1: the observed order is undefined; r must exceed 1.- Reporting the GCI as a percentage when the function returns a fraction.- Trusting the extrapolated value when the observed order is near zero: r**p - 1 collapses and the estimate is garbage.- Treating an oscillatory or diverging sequence as quantifiable: order, extrapolated value, and GCI are None when the sequence is not monotone.## Behavior contract (gate 3)The grid convergence logic is exercised by the gate 3 contract test:scripts/test_convergence_verification.py againstscripts/convergence_verification_logic.py (stdlib unittest,offline). Run:python3 scripts/test_convergence_verification.py## Compliance- NACA Report 824 is US government work (public domain); summary and physics values only, per standards-map.yaml. Convergence verification is generic numerical methodology: Richardson extrapolation and the GCI are standard discretization error estimation, not RTCA or SAE content.- compliance: STANDARDS-REF, gated: false.

Frequently asked questions