Roe scheme for general equation of state
 

Are there papers about Roe average and Roe scheme for general equation of state ? For example, pressure can be written as function of density and entropy, pressure=p(density,entropy).

Re: Roe scheme for general equation of state
 

Try to look at this references;

** D. L. Roberts, and M. S. Selim, "Comparative Study of Six Explicit and Two Implicit Finite Difference Schemes for Solving One-dimensional Parabolic Partial Differential Equations", International Journal for Numerical Methods in Engineering, 20(5), 817-844, 1984.

** A. Rigal, and G. Aleix, "Stability Analysis of Some Finite Difference Schemes for the Navier-Stokes Equations", International Journal for Numerical Methods in Engineering, 12(9), 1399-1405, 1978.

** John C. Strikwerda, "High-order-accurate schemes for incompressible viscous flow", International Journal for Numerical Methods in Fluids, 24(7), 715-734, 1997.

** P. Tamamidis, and D. N. Assanis, "Evaluation of Various High-order-accuracy Schemes with and without Flux Limiters", International Journal for Numerical Methods in Fluids, 16(10), 931-948, 1993.

** M. K. Patel, and N. C. Markatos, "An Evaluation of Eight Discretization Schemes for Two-dimensional Convection-Diffusion Equations", International Journal for Numerical Methods in Fluids, 6(3), 129-154, 1986.

** M. K. Patel, N. C. Markatos, and M. Cross, "A Critical Evaluation of Seven Discretization Schemes for Convection-Diffusion Equations", International Journal for Numerical Methods in Fluids, 5(3), 225-244, 1985.

** Alexander G. Churbanov, Andrei N. Pavlov, and Peter N. Vabishchevich, "Operator-splitting methods for the incompressible Navier-Stokes equations on non-staggered grids. Part 1: First-order schemes", International Journal for Numerical Methods in Fluids, 21(8), 617-640, 1995

**Carlos M. Lemos, "Higher-order schemes for free surface flows with arbitrary configurations", International Journal for Numerical Methods in Fluids, 23(6), 545-566, 1996. Best Regards

Mehdi Ben Elhadj

Applied mathematics laboratory

National Engineering School of Tunisia (E.N.I.T)

Re: Roe scheme for general equation of state
 

Is it necessary to use Roe average and Roe scheme in case of some unusual EOS?

Alternative way is to use approximate characteristic-based Riemann solvers instead. One of them (referred as LCS) can be found at

www.geocities.com/MotorCity/Pit/9939/freecfd.htm

- a source code in C and short description in PostScript.

Generalization of the solution procedure will affect the way you compute speed of sound

c_s = c_s( pressure, entropy ) = sqrt( dp / dr )

- the particular EOS is needed!

Best wishes,

Andrei

Re: Roe scheme for general equation of state
 

For a general EOS, the Roe average becomes non-unique. A one-parameter family can be found. Most papers on this subject deal with the problem of what is the "best" choice. In practice, most of them work well.

I dont have the references handy, but the authors are:

1) P. Glaister, JCP.

2) J. S. Shuen, B. Ban Leer, M. S. Liou, JCP

3) B. Larrotoru.

4) M. Vinokur and Liu. JCP

Hope this helps.

A. Suresh