Non-uniqueness of almost unidirectional inviscid compressible flow

Pavel Šolín; Karel Segeth

Applications of Mathematics (2004)

  • Volume: 49, Issue: 3, page 247-268
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Šolín, Pavel, and Segeth, Karel. "Non-uniqueness of almost unidirectional inviscid compressible flow." Applications of Mathematics 49.3 (2004): 247-268. <http://eudml.org/doc/33184>.

@article{Šolín2004,
abstract = {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.},
author = {Šolín, Pavel, Segeth, Karel},
journal = {Applications of Mathematics},
keywords = {non-uniqueness; inviscid gas flow; compressible Euler equations; quasi-one-dimensional; axisymmetric; finite volume method; non-uniqueness; inviscid gas flow; compressible Euler equations},
language = {eng},
number = {3},
pages = {247-268},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Non-uniqueness of almost unidirectional inviscid compressible flow},
url = {http://eudml.org/doc/33184},
volume = {49},
year = {2004},
}

TY - JOUR
AU - Šolín, Pavel
AU - Segeth, Karel
TI - Non-uniqueness of almost unidirectional inviscid compressible flow
JO - Applications of Mathematics
PY - 2004
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 49
IS - 3
SP - 247
EP - 268
AB - 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.
LA - eng
KW - non-uniqueness; inviscid gas flow; compressible Euler equations; quasi-one-dimensional; axisymmetric; finite volume method; non-uniqueness; inviscid gas flow; compressible Euler equations
UR - http://eudml.org/doc/33184
ER -

References

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