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Hey, Nasser here 👋

In CFD, “convergence” is a numerical concept most users think they understand.

A Google / ChatGPT definition will return something like:

“CFD convergence is the point in an iterative simulation where the numerical solution stabilizes, meaning calculated flow variables (like velocity, pressure, temperature) stop changing significantly with each iteration, indicating the solution is approaching a stable, reliable answer for the physical problem being modelled.”

We have the general idea, but the complete (most useful) picture is missing.

Yes, the errors in the iterative solution should be reducing over time / each iteration.
But no, it doesn’t necessarily mean we have a “reliable” answer for the physics problem being simulated.

And this is the key point.

What OpenFOAM is really doing

When you run the solver (simpleFoam, pimpleFoam etc), OpenFOAM isn’t solving the Navier-Stokes equation.

At least not directly.

Instead it discretises the problem into algorithmic equations that represent those physical laws.

So, when OpenFOAM prints to the console:

Solving for Ux, Initial residual = 1e-06, Final residual = 1e-08

It means:

  • a linear system was solved to a tolerance (either default or user-set)

  • it did it for for the current iteration

  • it did it using the current approximations of all other fields

It does not mean:

  • the physics is correct

  • the model is valid

  • the result is defensible

It actually means:

“The algebraic system I constructed is self-consistent.”

That’s all.

Nothing more. Nothing less.

Wave height on a column simulated using OpenFOAM, source: NextFoam

When you really understand this you’ll never simply take a good-looking residuals plot at face value ever again.

I always recommend independent values like the Nusselt number for thermal cases or the Drag coefficient for aerodynamic cases be monitored for greater confidence in your simulation results.

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