Over the years I’ve noticed that one of the most common traps, especially for those new to CFD, is treating residuals as the sole indicator of convergence. I’ve fallen into this myself, chasing residuals down to 1e-6 or lower, while completely ignoring whether the physics of the solution made any sense.

A recent project reminded me of this issue. I was running an external aerodynamics case on a moderately complex geometry using a pressure-based solver. The residuals for continuity and momentum dropped nicely — textbook convergence. But when I checked the integrated forces, the lift coefficient was oscillating by nearly 8% between iterations. In other words, the solver was happy, but the physics was not.

After digging deeper, I realized the following points (worth sharing for discussion):

1. Residuals ≠ Convergence
2. They tell you whether the equations are being satisfied numerically, not whether the flow solution is stable or accurate.
   
3. Monitor Flow Quantities
4. Integrated variables like drag, lift, heat transfer coefficients, or pressure drop across a section are often better indicators of when the solution has stabilized.
   
5. Physical Plausibility Check
6. In my case, I compared the results against empirical data and simpler analytical estimates (thin airfoil theory, in this example). The trend was way off until I refined the mesh near the leading edge.
   
7. Mesh Independence is Critical
8. I had assumed my grid density was “good enough” because the y+ values looked reasonable. But force oscillations only disappeared after refining local wake regions.

I’m curious how others approach this balance. Do you set a residual threshold (say 1e-4 or 1e-5) as a hard rule? Or do you mostly rely on monitoring physical quantities like forces, mass flow balance, or energy conservation?

For me, the biggest takeaway is: residuals are necessary, but not sufficient. A simulation with low residuals but unrealistic physical results is just as bad as one with diverging equations.

Looking forward to hearing how the community here tracks and validates convergence in real-world cases.