Geodesic
Non-uniqueness of almost unidirectional inviscid compressible flow
Applications of Mathematics, Tome 49 (2004) no. 3, pp. 247-268.

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Our aim is to find roots of the non-unique behavior of gases which can be observed in certain axisymmetric nozzle geometries under special flow regimes. For this purpose, we use several versions of the compressible Euler equations. We show that the main reason for the non-uniqueness is hidden in the energy decomposition into its internal and kinetic parts, and their complementary behavior. It turns out that, at least for inviscid compressible flows, a bifurcation can occur only at flow regimes with the Mach number equal to one (sonic states). Analytical quasi-one-dimensional results are supplemented by quasi-one-dimensional and axisymmetric three-dimensional finite volume computations. Good agreement between quasi-one-dimensional and axisymmetric results, including the presence of multiple stationary solutions, is presented for axisymmetric nozzles with reasonably small slopes of the radius.
DOI : 10.1023/B:APOM.0000042365.99783.b3
Classification : 35L65, 65H10, 76H05, 76M25, 76N10, 76N15
Keywords: non-uniqueness; inviscid gas flow; compressible Euler equations; quasi-one-dimensional; axisymmetric; finite volume method 
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Šolín, Pavel; Segeth, Karel. Non-uniqueness of almost unidirectional inviscid compressible flow. Applications of Mathematics, Tome 49 (2004) no. 3, pp. 247-268. doi : 10.1023/B:APOM.0000042365.99783.b3. http://geodesic.mathdoc.fr/articles/10.1023/B:APOM.0000042365.99783.b3/

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