Frequently Asked Question

Typical variables with under-relaxation factors:

• Pressure
• Momentum (velocity components)
• Turbulence quantities (k, ε or ω)
• Energy/temperature (if applicable)

General guidance on tuning:

• Default values from your solver are usually a reasonable starting point — don't change them preemptively unless you have a convergence problem
• If the solution is diverging or oscillating wildly, lower the under-relaxation factors (more conservative, more stable, slower convergence)
• If convergence is very slow but stable, cautiously raising factors can speed things up — but do this incrementally, watching residual behavior closely after each change
• Pressure-velocity coupling schemes (like SIMPLE, SIMPLEC, or coupled solvers) also affect how sensitive the case is to under-relaxation settings — coupled solvers often tolerate higher relaxation factors than segregated ones

Solution methods:

• Segregated solvers solve each equation (momentum, pressure correction, etc.) sequentially, looping until convergence — generally more memory-efficient but can converge more slowly
• Coupled solvers solve pressure and momentum simultaneously — often converges faster and more robustly for many cases, at the cost of higher memory use per iteration

Practical troubleshooting order when convergence stalls:

1. Check mesh quality first (see Article 4) — many "solver" problems are actually mesh problems
2. Verify boundary conditions are physically sensible (see Article 5)
3. Lower under-relaxation factors incrementally
4. Consider switching from segregated to coupled solver (or vice versa) if persistently unstable
5. Reassess whether the case might genuinely be unsteady (see Article 2)

Engineering interpretation

Solver Settings & Under-Relaxation Factors should be treated as an engineering decision supported by a defined function, known inputs, declared assumptions, and an observable result. The first step is to identify the quantity or characteristic being predicted, measured, or controlled. Next identify the material, geometry, operating condition, process setting, or boundary condition that drives it. This prevents a calculation from being separated from the physical situation it is intended to represent.

Use the simplest model that captures the dominant mechanism, then check whether omitted effects could change the decision. Dimensional consistency, limiting cases, sensitivity to the dominant input, and comparison with an independent estimate are practical safeguards. If the result is used for a release decision, the measurement method, acceptance criterion, configuration, and evidence owner should be recorded with the result.

The expression is a reporting framework. It does not replace the governing relation for the specific problem. Inputs should have units and a declared source; assumptions should state what is neglected and why that omission is acceptable for the intended use.

Worked example

Suppose the requirement is a characteristic of 10.00 ± 0.10 mm. A production study records a mean of 10.02 mm and a within-process standard deviation of 0.02 mm. The nearest specification limit is 0.08 mm from the mean, or four standard deviations. The nominal result appears capable, but the engineer must still confirm measurement-system variation, process stability, material condition, and whether the sample represents the intended production window.

Engineering check: record the input data, revision, calculation, uncertainty, and reaction plan. A result is not engineering-grade merely because a formula produces a number.