Riemann solver
There are many approximate Riemann solvers for Godunov type schemes. Given the capability of modern computers, why not just stick to the exact iterative Riemann solver? Are there other issues concerned such as stability?
Shuo 
Re: Riemann solver
The exact Riemann's solver is more prefarable from a lot of points of v.. also from stability (you could find Prokopov articles and etc.), the main  the exact R.S. is a solution of the Fluid Structure Interaction problems, it is always stable, a problem  the exact R.S. for arbitrary state eq. (it is necessary to use numerecial integration for rarefaction wave)

Re: Riemann solver
In that case why bother using TVD I thought it was to minimise spurious oscillations near flow discontinuities.
Shuo 
Hi Shuo,
I am dealing with the same problem. Were you able to figure it out? Reply me at babuu.nishu@gmail.com Thanks 
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