Roe average
 

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

Re: Roe average
 

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

Re: Roe average
 

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?