Geodesic
Triple-deck analysis of formation and evolution of supersonic zones and local separation zones in unsteady transonic flow over a surface roughness element
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 45 (2005) no. 3, pp. 536-544

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Transonic gas flow over a small roughness element located on the surface of a plate is analyzed within the framework of the unsteady triple-deck theory, in which the potential flow in the outer region is described by the Lin–Reissner–Tsien equation. Special attention is given to the formation and evolution of supersonic zones and closing shock waves in the outer potential region and local separation zones in the lower viscous sublayer. It is found that two supersonic flow regions develop in the outer inviscid region. They are closed by shock waves and are connected to each other. The shock waves are inclined toward the incoming stream. Numerical computations agree well with the experimental data. 
@article{ZVMMF_2005_45_3_a16,
     author = {V. N. Diesperov and G. L. Korolev},
     title = {Triple-deck analysis of formation and evolution of supersonic zones and local separation zones in unsteady transonic flow over a~surface roughness element},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {536--544},
     publisher = {mathdoc},
     volume = {45},
     number = {3},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_3_a16/}
}
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V. N. Diesperov; G. L. Korolev. Triple-deck analysis of formation and evolution of supersonic zones and local separation zones in unsteady transonic flow over a surface roughness element. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 45 (2005) no. 3, pp. 536-544. http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_3_a16/