Preprint series: 03-08 , Preprints

MSC:

35L65 Conservation laws

35L67 Shocks and singularities, See also {58C27, 76L05}

76N99 None of the above but in this section

Abstract: The quasi-one-dimensional Euler equations in a duct of variable cross-section are probably one of the
most simplest non-conservative 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 non-unique. In order to
rule out the non-physical solutions, we provide 2D computations of the Euler equations in a duct of corresponding
geometry and compare it with the 1D results. Then, the physically relevant 1D solutions satisfy a kind of entropy
rate admissibility criterion. Finally, we present a procedure for finding an exact solution to the Riemann problem
and construct a Godunov-type method on its basis.

Keywords: Nozzle flow, nonstrictly hyperbolic, resonance, Godunov method

Upload: 2003-05-13-05-13