The most common response to "it will not converge" is to lower the relaxation factors. Sometimes that works. More often it hides the real cause and lets the solution creep towards a wrong answer. The order should be as follows.
1. Suspect the setup first
In most non-converging solutions the fault is not in the settings but in the inputs:
- Is the boundary condition physically consistent? Flow rate may have been imposed at both inlet and outlet.
- Is there reverse flow at the outlet? If so the solver cannot know what to do there, and the outlet needs to move downstream. See the boundary condition note.
- Are the material properties sensible? A viscosity entered in the wrong units cannot be rescued by any setting.
- Are there negative-volume or badly skewed cells? A single bad cell can stall the whole solution.
2. Then ask whether the physics is steady at all
If the monitored quantity oscillates with a regular amplitude, the problem may be transient, and no setting will make a steady-state solver converge on it. The way to tell them apart is in the convergence note.
3. Fix the initial condition
You do not have to start from nothing. A quick solution on a coarse mesh, or one obtained at a lower velocity or lower power, is an excellent starting point for the fine mesh. On difficult problems, ramping the load in steps — raising the flow rate, the power or the rotational speed gradually — can be enough on its own.
4. Drop the discretisation order temporarily
First-order schemes are stable but produce numerical diffusion, and the result blurs. The correct use is this: run the first few hundred iterations first order to settle the field, then switch to second order and converge there.
A solution left at first order looks converged and is wrong. Every result that goes into a report must have been obtained with a second-order scheme.
5. Relaxation factors last
If you have got this far, lowering the factors is legitimate. Two reminders:
- A relaxation factor changes the rate of convergence, not the solution. A solution converged with low factors and one converged with high factors must agree. If they do not, neither has converged.
- Do not lower them all at once. Touch the factor for whichever equation's residual is stalling; upsetting the balance between pressure and momentum makes convergence slower still.
What belongs in the report
The discretisation order used, the pressure-velocity coupling method, and the settings the final solution was obtained with. Without those three lines the result is not reproducible.
References
- Ferziger, J. H., Perić, M. & Street, R. L. (2020). Computational Methods for Fluid Dynamics, 4th ed. Springer. DOI: 10.1007/978-3-319-99693-6
- Celik, I. B., Ghia, U., Roache, P. J., Freitas, C. J., Coleman, H. & Raad, P. E. (2008). Procedure for estimation and reporting of uncertainty due to discretization in CFD applications. Journal of Fluids Engineering, 130(7), 078001. DOI: 10.1115/1.2960953