Hi Sajiv, 

You may find these articles useful:

Roache, P.J.. Verification of codes and calculations. AIAA Journal 1998;36(5):696–702. URL: http://dx.doi.org/10.2514/2.457. doi:10.2514/2.457.

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

Roache, P.J.. Perspective: A method for uniform reporting of grid refinement studies. Journal of Fluids Engineering 1994;116(3):405–413. URL: http://dx.doi.org/10.1115/1.2910291.

Best regards,

Shakun

Indeed, especially the third paper Shakun cited should work well.

You can also simply state what 'better' means in regards to the coarser mesh and construct the argument that way. For example, I require tolerance T which is met by grid G when compare to sub-grid g, and in this way, the computational efficiency by using G instead of g is X (where ‘better’ here is taken to be computational efficiency, but it could be a number of other objective functions).

I think you should evaluate your mesh result based on some parameters such as accuracy of solutions and computational effort. you can find some good explanation in this book:

Computational Fluid Dynamics: An Introduction for Engineers

By M. B. Abbott