Roe approximation for stiffed gas equation of state

nikkey · September 29, 2020, 10:02

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:

$P=(\gamma-1)e \rho + \gamma P_c$
where, P - pressure, $\gamma$ - ratio of specific heats, e - internal energy, $\rho$ - 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!

Eifoehn4 · September 29, 2020, 12:43

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.

mczero57 · November 21, 2020, 22:36

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

September 29, 2020, 10:02	Roe approximation for stiffed gas equation of state	#1
nikkey New Member Join Date: Sep 2020 Posts: 1 Rep Power: 0	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: $P=(\gamma-1)e \rho + \gamma P_c$ where, P - pressure, $\gamma$ - ratio of specific heats, e - internal energy, $\rho$ - 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!

September 29, 2020, 12:43		#2
Eifoehn4 Senior Member - Join Date: Jul 2012 Location: Germany Posts: 184 Rep Power: 13	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. nikkey likes this. __________________ Check out my side project: A multiphysics discontinuous Galerkin framework: Youtube, Gitlab.

Similar Threads
Thread	Thread Starter	Forum	Replies	Last Post
Domain Reference Pressure and mass flow inlet boundary	AdidaKK	CFX	75	August 20, 2018 05:37
Equation of state for water?	jinwon park	Main CFD Forum	2	December 20, 2007 07:32
continuity equation	Rafal	Main CFD Forum	4	November 29, 2006 09:27
Gas pressure question	Dan Moskal	Main CFD Forum	0	October 24, 2002 22:02
Roe scheme for general equation of state	zouchu	Main CFD Forum	3	August 10, 2000 16:46

November 21, 2020, 22:36		#3
mczero57 New Member sam Join Date: Jan 2011 Posts: 20 Rep Power: 15	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