# Nondimensional gas constants

I am doing a nondimensional Navier-Stokes simulation, but it's not exactly clear what values to use for the various gas constants: $R$, $C_v$, and $C_p$. Obviously, once I know one of these and $\gamma$, I can define the others. A colleague of mine is using the formula $$C_v=\frac{1}{\gamma*(\gamma-1)M_\infty^2}$$ but it's not clear where this comes from and what value to use for $M_\infty$, especially in the context of shock-tube problems. For lack of a better option, I've just been setting $M_\infty=1$, but I'm not convinced this is defensible. What do other people do in this context?

• What is $M_{\infty}$ here? Dimensional analysis suggests it must have units of reciprocal square root heat capacity, which would be unusual. – Geoff Oxberry Oct 9 '14 at 18:30
• @GeoffOxberry, for external flows, $M_\infty$ is the free stream Mach number, typically. I think there's something funny with this formula. – Bill Barth Oct 9 '14 at 19:26