Grid Convergence Index (GCI) Calculator

Quantify numerical uncertainty and verify grid independence in CFD simulations using Roache's methodology.

PublishedCalculatorengineering calculators

Governing Formulas

R=ϕ2−ϕ1ϕ3−ϕ2R = \frac{\phi_2 - \phi_1}{\phi_3 - \phi_2}
p=ln⁡∣(ϕ3−ϕ2)/(ϕ2−ϕ1)∣ln⁡rp = \frac{\ln | (\phi_3 - \phi_2) / (\phi_2 - \phi_1) |}{\ln r}
GCI21=1.25⋅ea21r21p−1GCI_{21} = \frac{1.25 \cdot e_a^{21}}{r_{21}^p - 1}

Grid 1 (Fine)

Grid 2 (Medium)

Grid 3 (Coarse)

Grid Convergence Index

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Awaiting Input

Use this as a quick diagnostic / starting point. Verify against your solver setup, mesh, timestep, model assumptions, and operating conditions. Results are approximations of numerical uncertainty. Always ensure iterative convergence is achieved before performing spatial grid convergence studies.

Want to learn more about convergence?

Read CFD Convergence: Why Residuals Are Not Enough →

Worked Example

Scenario: Airfoil Drag Calculation

You run an airfoil simulation on 3 progressively refined grids to compute the Drag Coefficient (Cd). You need to report the Grid Convergence Index (GCI) to quantify discretization uncertainty.

Example Inputs (Spacing Mode):
  • Grid 1 (Fine): Spacing = 0.01 m, Solution (Cd) = 0.98
  • Grid 2 (Medium): Spacing = 0.02 m, Solution (Cd) = 0.95
  • Grid 3 (Coarse): Spacing = 0.04 m, Solution (Cd) = 0.88

Interpretation:The convergence is monotonic. The Grid Convergence Index (GCI₂₁) is ~3.76%. You can report: "The numerical uncertainty in the fine-grid solution for Drag Coefficient is bounded by a GCI of 3.8%." The Asymptotic Range Ratio (R) is ~0.43, indicating you may need further refinement to reach the true asymptotic range (ideally R approaches 1.0).

Assumptions & limitations

Limitations

  • Methodology: Relies strictly on Roache's Methodology for Grid Convergence Index. A Factor of Safety (Fs = 1.25) is hardcoded since three grids are evaluated.
  • Error Dominance: Assumes spatial discretization errors dominate over temporal or iterative convergence errors. Iterative convergence must be achieved first.
  • Asymptotic Range: GCI equations are strictly valid only when solutions are in the asymptotic range of convergence.
  • Convergence State: GCI requires strictly monotonic convergence. Oscillatory or divergent states indicate fundamental mesh or setup problems and cannot be quantified by GCI.
  • Refinement Ratios: Refinement ratios near 1.0 (e.g., < 1.3) may produce unreliable error estimates due to round-off error contamination.

Related Resources

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