Check numerical accuracy across three refined grids quickly. Compute order, extrapolation, and uncertainty with clarity. Export results, compare cases, and document your simulations today.
Provide three grid spacings and the computed scalar quantity on each grid. The calculator will auto-order grids from fine to coarse.
Submit inputs to generate an interactive convergence plot. A preview appears here using example values.
This sample resembles a refined simulation where the monitored quantity stabilizes as the grid is refined.
| Grid level | Grid spacing (h) | Quantity (φ) | Typical interpretation |
|---|---|---|---|
| Fine | 0.010 | 1.2384 | Closest to grid-independent value |
| Medium | 0.014 | 1.2310 | Intermediate resolution |
| Coarse | 0.020 | 1.2195 | Higher discretization error |
r21 = h2 / h1r32 = h3 / h2p is estimated iteratively from the three solutions using a common grid-convergence scheme.
This captures how the error scales with grid spacing.
φ_ext,21 = φ1 + (φ1 − φ2) / (r21^p − 1)e_a21 = |(φ1 − φ2) / φ1|GCI21 = F_s · e_a21 / (r21^p − 1)GCI32 = F_s · e_a32 / (r32^p − 1)Discretization error can dominate total numerical uncertainty. A three-grid study gives evidence of grid independence. Many CFD and FEA teams report GCI to support decisions. Small GCI values reduce risk in design and validation.
Record a representative spacing for each grid level. Use consistent physics settings and solver tolerances. Track one scalar output, like drag or peak stress. Save h1, h2, h3 and φ1, φ2, φ3 for each case.
Apparent order p describes how fast the solution converges. Higher p often indicates cleaner asymptotic behavior. Many second-order schemes approach p near 2 in smooth regions. Low p can suggest under-resolution or inconsistent numerics.
GCI converts the fine-medium difference into a defensible uncertainty. It scales with the safety factor and refinement ratio. Engineers commonly start with Fs = 1.25 for three grids. Report GCI21 as a percent next to the final predicted value.
Many studies target r near 1.3 to 2.0 per refinement. Larger r increases separation but may waste coarse resources. Smaller r reduces signal and can hide convergence trends. Keep geometry and boundary layers consistent across grids.
Present φ1 with GCI21 as the numerical uncertainty band. Include p, r21, and the extrapolated value for transparency. Add a short table and a convergence plot for readability. Store exports in your project folder for auditing.
It depends on your acceptance criteria and physics sensitivity. Many teams aim for below 1% for key outputs. Use the same threshold across comparable cases. Always report the value, not just a pass label.
Equal ratios help, but the method can handle different ratios. Large differences can reduce stability in the order estimate. Try to keep r21 and r32 reasonably close. Consistency improves comparison across projects.
The method assumes a clear fine, medium, and coarse sequence. Reordering prevents mistakes when inputs are swapped. The smallest h becomes the fine grid automatically. Your φ values move with their corresponding h values.
Non-monotonic behavior can occur with complex numerics. The apparent order may become unstable or low. Try improving solver convergence and using better refinement. You may also monitor a different, smoother output quantity.
Yes, treat h as the time step Δt instead of grid spacing. Use three refined time steps with the same setup. Interpret the results as temporal discretization uncertainty. Ensure the simulation reaches comparable physical time states.
Log axes cannot display zero. The plot uses a very small positive h for the extrapolated marker. The extrapolated value still represents the zero-spacing limit. Use the numeric table for exact reporting.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.