it is an interesting question. for convergence studies in my opinion the Roaches index is a very good option ( Roache, P J. QUANTIFICATION OF UNCERTAINTY IN COMPUTATIONAL FLUID DYNAMICS,

Journal of Fluids Engineering,1997)

Mesh statistics is a good way to show how well your CAD (solid mechanics)/CFD (thermal/fluid mechanics) model is behaving under a certain set of conditions.

The best way, currently in use, which is seen in every paper/research manuscripts is the "Grid Independence Study". For thesis reports, it also comes with "Validation Study" - something that I did in my master's thesis.

What you do is to take up an existing case (preferably from a paper/thesis) and test the boundary conditions for your model or various mesh sizes which you will be varying. My thesis supervisor advised to take at least 4 - 5 mesh sizes to conduct a sound mesh convergence study. One physical parameter - in case of the flow study (pressure/temperature/velocity/force) at a specific location (midspan/mid-pitch region etc) is compared for various mesh sizes and a simple mesh size (X) vs physical parameter considered (Y) is plotted. When two values of Y converge with either increasing or decreasing X, then the mesh convergence study is completed. This can also be conducted with your own test conditions, rather than existing cases. However, the validation and grid independence is best verified using existing cases. A deviation from 1% - 5% between your results and published one exhibits excellent modelling and mesh accuracy, 5% - 10% is also acceptable.

Hope this makes it clear.

I agree with Ruben. Richardson extrapolation method is suited for this. You will find the paper here

http://ftp.demec.ufpr.br/CFD/bibliografia/erros_numericos/Roache_1997.pdf

Mesh Sensitivity:

The best and most accurate way is by Direct (Analytical) Differentiation, if permitted. Otherwise, agreeing with Ruben, the paper by Roache is the most suitable for topic ;

( QUANTIFICATION OF UNCERTAINTY IN COMPUTATIONAL FLUID DYNAMICS).

Cheers

Thanks for your observations Prof Tapan. One has to look at other errors like dispersion(yyour book itself is a good source for it) and paralellisation errors.

Cheers

Yes, the book is a welcome publication and the research publications following the book are important contributions.