On the solution to the Riemann problem for the compressible duct flow

The quasi-one-dimensional Euler equations in a duct of variable cross section form probably one of the simplest nonconservative systems. We consider the Riemann problem for it and discuss its properties. In particular, for some initial conditions, the solution to the Riemann problem appears to be nonunique. In order to rule out the nonphysical solutions, we provide two-dimensional computations of the Euler equations in a duct of corresponding geometry and compare them with the one-dimensional (1D) results. Then, the physically relevant 1D solutions satisfy a kind of entropy rate admissibility criterion.