the unsteady euler eq is hyperbolic and Riemman problem solver is widely used in solving the hyperbolic equation by FVM. But what's class of steady euler equation? I am working on solving shallow water eq, which I think the classification is dependent of frude number, maybe hyperbolic, maybe elliptical or parobolic. So I personally think for steady euler eq or shallow water eq is unsolvable, some body can give some reliable paper or reference to prove what i thought is wrong or not. thanks .

You should also solve unsteady equations for steady flow problem (using local time steps).

dQ/dt=R

where R is the residual. When R is approaching zero, you get a steady solution. Hence, you still solve a hyperbolic problem.

Hope this helps

Li

thank u sir. yes, it's one popular way to deal with steady problem but time consuming. Can we just start the steady equation?

I think the easier way to solve a steady equation is to make it unsteady. The reason behind this is probably because this makes the equation hyperbolic. Better explanations must be stated in some CFD text books somewhere but I don't have any of them in hand.