I am solving the Riemann problem for 1-D shallow water equations. I used the generalized Riemann invariants to obtain the values of the water depth and velocity in the star region. Do you think this is the right method? When I plotted the result I see 2 shock waves moving( with time) in opposite directions for both depth and velocity .
But as I kept reading the book(Shock capturing methods by E.F. Toro), it seems like one has to understand the Nature of the eigenvalues(wave types) of the system, before one would know the condition(s) to apply.
Do I need to know if each wave is a shock, rarefraction or shear wave before employing the relevant conditions?
Please kindly advise me.