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 Onedimensional Parabolic Partial Differential Equations", International Journal for Numerical Methods in Engineering, 20(5), 817844, 1984. ** A. Rigal, and G. Aleix, "Stability Analysis of Some Finite Difference Schemes for the NavierStokes Equations", International Journal for Numerical Methods in Engineering, 12(9), 13991405, 1978. ** John C. Strikwerda, "Highorderaccurate schemes for incompressible viscous flow", International Journal for Numerical Methods in Fluids, 24(7), 715734, 1997. ** P. Tamamidis, and D. N. Assanis, "Evaluation of Various Highorderaccuracy Schemes with and without Flux Limiters", International Journal for Numerical Methods in Fluids, 16(10), 931948, 1993. ** M. K. Patel, and N. C. Markatos, "An Evaluation of Eight Discretization Schemes for Twodimensional ConvectionDiffusion Equations", International Journal for Numerical Methods in Fluids, 6(3), 129154, 1986. ** M. K. Patel, N. C. Markatos, and M. Cross, "A Critical Evaluation of Seven Discretization Schemes for ConvectionDiffusion Equations", International Journal for Numerical Methods in Fluids, 5(3), 225244, 1985. ** Alexander G. Churbanov, Andrei N. Pavlov, and Peter N. Vabishchevich, "Operatorsplitting methods for the incompressible NavierStokes equations on nonstaggered grids. Part 1: Firstorder schemes", International Journal for Numerical Methods in Fluids, 21(8), 617640, 1995 **Carlos M. Lemos, "Higherorder schemes for free surface flows with arbitrary configurations", International Journal for Numerical Methods in Fluids, 23(6), 545566, 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 characteristicbased 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 nonunique. A oneparameter 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 
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