I am currently studying the approximate linear solver of Roe for the Riemann problem. I have formulae for Roe's averaged density, velocity and total enthalpy, but, as my flux Jacobians are written in terms of conservative variables, I need formulae for Roe's averaged mass flux and for total energy times density. As for the first one, I obviuously obtain R[rho*u]=R[rho] * R[u] ( R[ ] means Roe's average). What for R[E]? Do I use the same scheme used for u and H, thus obtaining R[E]=(E1*sqrt(rho1)+E2*sqrt(rho2))/ (sqrt(rho1)+sqrt(rho2)) ?

Thanks in advance, Andrea

Knowing H, rho and u, you have enough variables to determine all your unknowns. Just find the primitive variables from the latter three averaged properties and obtain E from the primitives..

You can check the exactness of your Roe average by multiplying the Roe averaged A and (F_R-F_L) and comparing the so-obtained flux to (Q_R-Q_L). They should match exactly.

-bernard

Thanks for your interest in my question. I did not answer immediately because I wanted to try your suggestion first. Anyway, I did not obtain convergence even in this way, so I wuold like to ask you some questions: I understand A is the flux Jacobian, but which are F_R and F_L? Maybe they the solution vector in the cell on the right and in the cell on the left, aren' t they? And which are Q_R and Q_L? Lastly, as Roe's average ( harmonic average ) is nonlinear, I should not obtain the same result using your method and mine. Could you indicate me some references where the question is discussed in detail?