[JuPa]

There are a ton of books out there on statistics and CFD.

Are there any you can recommend personally?

I'm not a big fan of doing simulations just to generate Colours For Directors etc.,

I want to use more statistical methods such as Fourier analysis, standard deviations to gauge my CFD analysis

I know what each of those mean in theory - but when it comes to applying it to CFD it appears to be somewhat of a dark art.

[ghorrocks]

I recommend you look into validation and verification of CFD results. This is a topic of research in itself - It looks into questions like: How can you assess the accuracy of a CFD model? What mesh/convergence criteria/time step size should I use to get a result of a known accuracy?

It also introduces concepts like Richardson extrapolation which allow you to use a mesh refinement study to extrapolate your results to zero mesh size (ie totally grid independant results).

The key author in this field is Roache, and his text book "Computational Fluid Dynamics". The book is a little old now but is still a classic. Authors like Celik have extended his work more recently. This FAQ link is to a paper by Celik: https://www.cfd-online.com/Wiki/Ansy...publishable.3F

Also look up concepts like grid convergence index (GCI).

[JuPa]

Thanks Glenn.

I use the CGI method a lot (thanks to you!) - there's a paper out there by Celik et al (Journal of Fluid Mechanics Editorial Policy) on how to obtain proper grid independent results.

I'm more after stuff like if you set monitor points of velocity and torque and those values repeat cyclically; could you then do Fourier statistical analysis on them?

Additionally if you have 5 input variables and 10 output variables what's the relationship? Which variable is the most effective? I know Ansys does this in Design Explorer - I don't think their version is very good - the Star CCM+ version HEEDS is excellent for this kind of thing. I don't want to rely on Ansys or Star though - I want to know exactly what the optimiser is computing and how (i.e. theory in a text book).

[ghorrocks]

I'm more after stuff like if you set monitor points of velocity and torque and those values repeat cyclically; could you then do Fourier statistical analysis on them?

This is quite a specialised application, the approaches by Roache and Celik are quite general. Yes, you can do Fourier analysis of any pattern, particularly a cyclical one - but it will just tell you the frequency components of the pattern you gave it. I can't see how you can use that to estimate accuracy or convergence. But it would be an interesting area to do some literature research on.

Additionally if you have 5 input variables and 10 output variables what's the relationship?

This question is more about multi-variable models and optimisation, and I don't see an application to CFD verification and validation. If I have missed something let me know.

Multi-variable optimisation is a research topic in itself. It is used in many applications other than CFD, as optimisation is a common problem in many applications.

Matlab and Python (in the scipy module) have lots of built in optimisation tools with good descriptions of how they work. They could be good places to start.

[JuPa]

Thanks Glenn. I'll do some digging and report back in a few months.