Geodesic
A technique for the numerical analysis of the riblet effect on the temporal stability of plane flows
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 6, pp. 1109-1125

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Problems related to the temporal stability of laminar viscous incompressible flows in plane channels with ribbed walls are formulated, justified, and numerically solved. A new method is proposed whereby the systems of ordinary differential and algebraic equations obtained after a spatial approximation are transformed into systems of ordinary differential equations with a halved number of unknowns. New algorithms that effectively calculate stability characteristics, such as the critical Reynolds numbers, the maximum amplification of the disturbance kinetic energy density, and optimal disturbances are described and substantiated. The results of numerical experiments with riblets similar in shape to those used in practice are presented and discussed. 
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     author = {A. V. Boǐko and Yu. M. Nechepurenko},
     title = {A technique for the numerical analysis of the riblet effect on the temporal stability of plane flows},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
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     publisher = {mathdoc},
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     number = {6},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_6_a10/}
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A. V. Boǐko; Yu. M. Nechepurenko. A technique for the numerical analysis of the riblet effect on the temporal stability of plane flows. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 6, pp. 1109-1125. http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_6_a10/