Criteria for nonuniqueness of Riemann solutions to compressible duct flows. (English) Zbl 1277.76091
Summary: The Riemann solutions without vacuum states for compressible duct flows have been completely constructed in [E. Han et al., J. Hyperbolic Differ. Equ. 9, No. 3, 403–449 (2012; Zbl 1263.35178)]. However, the nonuniqueness of Riemann solutions due to a bifurcation of wave curves in state space is still an open problem. The purpose of this paper is to single out the physically relevant solution among all the possible Riemann solutions by comparing them with the numerical results of the axisymmetric Euler equations. N. Andrianov and G. Warnecke [SIAM J. Appl. Math. 64, No. 3, 878–901 (2004; Zbl 1065.35191)] suggested using the entropy rate admissibility criterion to rule out the unphysical solutions. However, this criterion is not true for some test cases, i.e. the numerical result for axisymmetric three dimensional flows picks up an exact solution which does not satisfy the entropy rate admissibility criterion. Moreover, numerous numerical experiments show that the physically relevant solution is always located on a certain branch of the L-M curves.
MSC:
| 76N10 | Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics |
| 35A02 | Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness |
| 76M99 | Basic methods in fluid mechanics |
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