hi, could some one tell me what an entropy function is.. and also give a bit of physical insight with examples? and how does one know whether an entropy fix is required for a numerical scheme? thanking you

The entropy fix has been there for a long time.The computational fluid mechanics and heat transfer book of pletcher et al provides detailed information on when it is needed.

You've got the answer for the first part of the question in my previous reply. To find out if the Riemann solver needs an entropy fix, all solutions must be examined to see if there are any unphysical solutions admitted by the formulation. Expansion shock is a famous non-physical solution admitted by Euler equations.