Mesh Refinement Ratio Calculator for CFD Grid Studies

Many CFD mesh refinement studies need a representative refinement ratio before applying Richardson extrapolation or the Grid Convergence Index. If only total cell counts are available, an equivalent grid-size refinement ratio can be estimated using the spatial dimension.

Governing Formulas

r_{21} = \left(\frac{N_2}{N_1}\right)^{\frac{1}{d}} \quad \text{or} \quad r_{21} = \frac{h_1}{h_2}

r_{32} = \left(\frac{N_3}{N_2}\right)^{\frac{1}{d}} \quad \text{or} \quad r_{32} = \frac{h_2}{h_3}

Refinement Ratio

Awaiting Input

Grid Convergence Index

Quantify numerical uncertainty →

Richardson Extrapolation

Estimate grid-independent value →

Worked Examples

Example A — 3D Cell-Count Mode

For 3D meshes, doubling the number of cells does not mean the grid spacing was refined by a factor of 2; the equivalent spacing ratio is based on the cube root of the cell-count ratio.

Example Inputs:

Coarse cells: 250,000
Medium cells: 500,000
Fine cells: 1,000,000
Dimension: 3D

Interpretation: The ratios are consistent because the cell count doubles in each refinement step. However, the equivalent linear grid refinement ratio is only ~1.26, not 2.

Example B — Representative Mesh-Size Mode