Roe approximation for stiffed gas equation of state
 

Good day,

I want to implement Euler equations finite volume scheme for compressible nonlinear liquid based on stiffed gas equation of state (EOS) of the form:


where, P - pressure, - ratio of specific heats, e - internal energy, - density, - stiffness parameter.

I would like to use Roe approximate Riemann solver, the same way as discussed in the original Roe's paper. For it, I first need to calculate the Jacobian for Euler system. However, it seems that the Jacobian has the same form as for ideal gas EOS. Does this mean that I can use the same approach for stiffed gas EOS as for ideal gas EOS (same wave strength, right eigenvectors), with the only difference that Roe averages of speed of sound and enthalpy for stiffed gas EOS will be a bit different?

Thank you in advance!

Yes, there should be no difference as along as both sides of the Riemann problem consists of the same EOS.

Note that this is not the case for real equations of state.

Hello Nikkey,

If both gamma and Pc are constants, then you are just adding a constant to the pressure and that should not change anything. Just make sure that this EOS makes sense thermodynamically - ie entropy and enthalpy, etc. are well defined.

Thanks
Sam