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?
Nondimensional gas constants
fluid dynamics;navier stokes
If you are using an ideal gas equation of state, only the ratio of specific heats should appear in the nondimensional governing compressible  Navier-Stokes equations. Knowing that you want to simulate (say) air, which provides gamma, is sufficient.If this is your setting and my answer unclear, please let me know and I can point you to a write up.