Geodesic
Direct numerical simulation of the laminar-turbulent transition at hypersonic flow speeds on a supercomputer
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 8, pp. 1347-1373

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A method for direct numerical simulation of three-dimensional unsteady disturbances leading to a laminar-turbulent transition at hypersonic flow speeds is proposed. The simulation relies on solving the full three-dimensional unsteady Navier–Stokes equations. The computational technique is intended for multiprocessor supercomputers and is based on a fully implicit monotone approximation scheme and the Newton–Raphson method for solving systems of nonlinear difference equations. This approach is used to study the development of three-dimensional unstable disturbances in a flat-plate and compression-corner boundary layers in early laminar-turbulent transition stages at the free-stream Mach number M = 5.37. The three-dimensional disturbance field is visualized in order to reveal and discuss features of the instability development at the linear and nonlinear stages. The distribution of the skin friction coefficient is used to detect laminar and transient flow regimes and determine the onset of the laminar-turbulent transition. 
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     author = {I. V. Egorov and A. V. Novikov and A. V. Fedorov},
     title = {Direct numerical simulation of the laminar-turbulent transition at hypersonic flow speeds on a supercomputer},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
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     publisher = {mathdoc},
     volume = {57},
     number = {8},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_8_a9/}
}
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I. V. Egorov; A. V. Novikov; A. V. Fedorov. Direct numerical simulation of the laminar-turbulent transition at hypersonic flow speeds on a supercomputer. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 8, pp. 1347-1373. http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_8_a9/