Is there any approximate Riemann Solver, that does not rely on direct computation of eigenvalues of the flux Jacobian?
You need the wave speeds (eigenvalues) to compute the diffusion term in your flux - but you don't need the jacobian. When using general equation of state we estimate the wave speed and then use that in an hlle, local lax or other flux.
Yes John, we really do. I was wondering if there is any new innovations that avoid that computation. Thanks.
John gave you the answer -- if you choose a flux like a local Lax-Friedrich flux all you need is an estimate of the maximum wave speed (locally or globally). But you get what you pay for -- such a flux is very dissipative. If you use a low order scheme and you want to do better you need the eigenvalues of the Jacobian for a Roe flux or something more advanced (and problem dependent).
Dear Jan, l like get something clearer. Is there any difference between estimated wave speed(max or min and global or local) and the eigenvalues(max or min and local or global)?
Chinedu,
The maximum wavespeed is naturally the same as the maximum (in magnitude) eigenvalue -- however all that is required for stability is that you have an upper bound for the wave speed -- that is sometimes easier to do.
Jan
Yes there is: look at this paper by P, Degond et al.
http://www.sciencedirect.com/science/article/pii/S0764444299801943
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