Grid Convergence Index GCI Calculator

CFD verification & validation (ASME V&V 20): Quantify spatial discretization error using Richardson extrapolation, calculate apparent convergence order ($p$), and compute the Grid Convergence Index ($GCI$).

Three-Grid Refinement Study

Fine Grid 1 Spacing h₁ (or N₁): Relative spacing (Finest mesh)

Fine Grid Solution f₁: e.g. Lift / Drag coefficient Cd

Medium Grid 2 Spacing h₂: Intermediate mesh (r₂₁ = h₂/h₁)

Medium Grid Solution f₂: Medium mesh target metric

Coarse Grid 3 Spacing h₃: Coarsest mesh (r₃₂ = h₃/h₂)

Coarse Grid Solution f₃: Coarsest mesh target metric

Safety Factor F_s: ASME standard = 1.25 for 3 grids

Formal Discretization Order: Theoretical solver scheme order

GCI Uncertainty & Extrapolated Solution

Fine Grid Uncertainty (GCI₂₁)

Richardson Extrapolated (f_ext)

Zero-grid spacing estimate (h → 0)

Apparent Order of Accuracy (p)

Calculated convergence rate

Asymptotic Range Check

GCI ratio (Target ≈ 1.0)

Medium Grid Uncertainty (GCI₃₂)

Coarse-to-medium error band

Monotonicity Ratio (R)

Convergence behavior

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Frequently Asked Questions

Why does ASME V&V 20 recommend a refinement ratio r >= 1.3?

If grid refinement is too small (e.g. r = 1.05), discretization errors are dwarfed by numerical round-off and incomplete iterative solver convergence, corrupting the calculation of apparent order p.

What is the asymptotic range of convergence?

The asymptotic range occurs when grid spacing is small enough that higher-order truncation error terms become negligible. When satisfied, GCI_32 / (r^p · GCI_21) approaches 1.0.

How is representative grid spacing h calculated for unstructured 3D meshes?

For an unstructured 3D mesh with N total cells across domain volume V: h = (V / N)^(1/3).