Frequently Asked Question

CFD error has several sources. Iterative error remains because the algebraic equations are not solved exactly. Discretization error arises from approximating derivatives or fluxes on a finite mesh and time step. Modeling error comes from simplifying unresolved physical processes.

Reduce these errors with different evidence: tighter convergence and balances for iterative error, grid/time refinement for discretization error, and validation or model comparison for modeling error. Do not combine all effects into one unexplained safety factor.

Numerical error and convergence

A numerical solution approximates the continuous conservation laws on a finite set of cells or control volumes. Discretization error depends on characteristic size, stretching, skewness, alignment, interpolation, boundary treatment, and the output being measured. Iterative convergence is different from mesh convergence: a solver can reduce algebraic residuals while the engineering quantity continues to drift.

φ is the reported quantity and h is a characteristic mesh size. Use an analytical or benchmark reference when possible; otherwise report a systematic refinement study.

Worked example

A pressure drop is 104 Pa on a coarse grid, 101 Pa on a medium grid, and 100 Pa on a fine grid. The medium-to-fine change is approximately 1%, while the coarse-to-medium change is approximately 3%. Report mesh sizes, refinement ratio, residual state, and whether the 1% change meets the design tolerance.

Check: refine where gradients or the engineering output are sensitive, not only where the global cell count is convenient.