Notes on Roache (1997)

Roache, P. J. (1997). Quantification of uncertainty in computational fluid dynamics. Annual Review of Fluid Mechanics, 29(1), 123-160.

Introduction

This is a review paper on the quantification of uncertainty within computational fluid dynamics.

Note the use of final calculation in the first paragraph. This is trying to separate these errors from those of grid adaptation, for instance.

Discusses prohibition of methods of first order spatial accuracy. Much like a wave energy model then.

• Verification: “solving the equations right”
• Validation: “solving the right equations”

Another nice quote:

“a code cannot be validated; only a calculation”

Error Taxonomies (p127)

Roache is quite unique in defining (or critiquing) error taxonomies. I think it just shows how hard it is to do such a thing.

Note that the taxonomies in Mackay (2010) are a joke. He talks of random, mean internal and external errors which is all over the place.

I don’t understand all of the terminology, particularly ordering. OK, here is something that might help:

“The defining characteristic of the non- ordered approximation is that, as mesh size tends to zero, the algebraic equations do not converge to any continuum”

This is from Verification of Computer Codes in Computational Science and Engineering By Patrick Knupp, Kambiz Salari.

The paper then bangs on about verification techniques for a long time.

Time Accuracy Estimation (p151)

To be frank, there is not a lot of discussion about time evolving solutions in the V&V literature, so this is quite useful.

“Estimation of the numerical error of the time discretisation can be done in the same manner as the spatial errors, but simpler methods may also be used.”

He offers a method for producing error estimates, but basically warns that testing the time step of a code is very important too.

Cafe Curves (p153)

This is one of the few places I have ever seen Cafe Curves written about (cumulative area fraction error) and they are used to represent domain errors. It might be interesting to try and do it with our grids, perhaps, rather than just trying to do point estimates?

Obviously, there is some interest in what is going on in the point estimates, but the uncertainty in the global field is the final aim.

There is also some discussion of how the error norms are useful or not. These are the $L_{2}$ and $L_{\infty}$ norms.