Reimann problem
What's the difference between the Riemann problem and the shock tube?

Re: Reimann problem
The Riemann problem is a method and the shock tube is an example of the method.

Re: Reimann problem
I guess you have confusions about the concept of the Riemann problem.
Riemann problem is a problem containing one single wave. That is, u(x,t=0)=uL for x <x0 uR for x >x0 Like above, the problem is spatially divided by two region but constant. If it is not constant(i.e. uL(x),uR(x)), it is called the Generalized Riemann problem. The shock tube problem is a very famous example used to simulate such a riemann problem. The reason you confused may be the difference between the exact solution and the numerical solution of the Riemann problem. There are a number of books available on this issue. For example, computational gasdynamics written by Culbert B. Laney. Good luck 
Re: Reimann problem
is there any other example of the Riemann problem ?

Re: Reimann problem
A dam breaking in shallow water is one. Any problem governed by a hyperbolic equation has a Riemann problem (look up the theory of Riemann invariants in a book on pdes).

Re: Reimann problem
Do you think someone can see it in twophase flows ? any advice will be very much appreciated.

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