Frequently Asked Question

Steady-state CFD solves the time-independent forms of the fundamental conservation laws governing fluid motion.

The governing equations:

• Continuity (mass conservation): ensures mass entering a control volume equals mass leaving it
• Momentum (Navier-Stokes): relates fluid acceleration to pressure gradients, viscous forces, and body forces (like gravity)
• Energy (if heat transfer is modeled): conservation of thermal energy, including convection and conduction
• Turbulence transport equations (if using a turbulence model): additional equations for turbulent kinetic energy, dissipation rate, or specific dissipation rate, depending on the model chosen

In steady-state mode, the time-derivative term (∂/∂t) is dropped from each equation, and the solver instead uses iterative methods to converge on a solution where all equations are satisfied simultaneously across the domain.

What convergence means: The solver doesn't produce an exact answer in one pass — it iterates, refining the solution field each cycle, and convergence means those iterations have stopped meaningfully changing the result.

Key convergence indicators to monitor:

• Residuals — numerical measure of how much each equation is still "unbalanced" at each cell; residuals should drop several orders of magnitude (commonly to 1e-3 to 1e-6 depending on required accuracy) and then flatten out
• Monitor points — tracking a specific output value (drag coefficient, outlet temperature, pressure drop) over iterations; a converged solution shows this value stabilizing to a constant
• Mass/energy imbalance — the difference between what flows into and out of the domain should approach zero

A common pitfall: Low residuals alone don't guarantee a correct or converged solution. Always cross-check with a monitored engineering quantity (like force coefficients or outlet averages) — if residuals look flat but your quantity of interest is still drifting, the solution hasn't truly converged yet.

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.