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).

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)

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

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