All CFD is wrong

Your CFD is wrong.

My CFD is wrong.

In fact, all CFD is wrong. But isn’t that a dangerous thing for someone who makes his living doing CFD to say? Not really and here’s why.

How many of you have heard of George E. P. Box? Not too many? Well, in the announcement of his passing, aged 93 in 2013, he was described as “one of the most important statisticians of the past century”. Not only did he leave a legacy including some heavyweight statistical textbooks. But he also left a couple of aphorisms that all CFD-ists should know.

This one captures the general gist:

Remember that all models are wrong; the practical question is how wrong do they have to be to not be useful.

— Empirical Model-Building and Response Surfaces (1987)

So, if you accept that your simulations are going to be wrong, then increasing their usefulness would seem like a smart thing to do. But do you have to choose between accuracy and utility? Surely the more accurate the model the more useful it becomes — doesn’t it?

In a word…no

In the CFD world, chasing increased accuracy sometimes has unintended consequences. Cell counts spiral upward, hardware requirements escalate and turnaround times lengthen. Maybe we add back some of the features we defeatured earlier (time spent taking them out & adding them back in — double-bubble)? Perhaps we increase the mesh resolution? Maybe a more expensive turbulence model? These time and cost increases can often make the results of a simulation less useful — oops, that’s not what we intended.

Good Enough?

The peak in the utility & accuracy tradeoff could be labelled good enough. But where is good enough? The above graph could be skewed either way along the accuracy axis. But at some point our quest for accuracy will make our model less useful.

Unfortunately, you can’t judge utility outside of the context of the problem you’re trying to solve. Useful is not an absolute. It’s only by understanding the problem your attacking that you can work out what’s useful.

Clients usually value utility over accuracy — if isn’t useful then they aren’t all that happy to pay for it. Worst case, they won’t realise it isn’t useful until they’ve gone away & had time to think about it. Say goodbye to future work from that client.

Shall we just give up on the modelling career then?

If that’s catwalk modelling then maybe. But don’t give up on the mathematical modelling just yet. Over to our new favourite statistician:

Since all models are wrong the scientist cannot obtain a correct one by excessive elaboration… Just as the ability to devise simple but evocative models is the signature of the great scientist so over-elaboration and over-parameterization is often the mark of mediocrity.

— Science and Statistics (1976)

No one is suggesting that everything can be reduced to a function in Excel. Or worse, that we shouldn’t model anything. But rather that we should be useful first & clever later.

I’ve mentioned the “five whys” before when I wrote about how we practice lean CFD. Try repeatedly asking “Why?” before increasing the model size, or the geometry complexity or hardware requirement. If it doesn’t lead to a more useful model then leave it alone and focus on getting the most out of what you’ve got. This is an example of using a minimum viable model approach.

There will always be models that are bigger, more complex, and/or more accurate than yours. Just as there will always be people rocking more processors and turning models around faster. But remember they’re still just models.

Maybe the question we should be asking ourselves is whether those bigger / more complex / more accurate models are more useful than ours?