Geodesic
Direct numerical simulation of laminar-turbulent flow over a flat plate at hypersonic flow speeds
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 6, pp. 1064-1081

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A method for direct numerical simulation of a laminar-turbulent flow around bodies at hypersonic flow speeds is proposed. The simulation is performed by solving the full three-dimensional unsteady Navier–Stokes equations. The method of calculation is oriented to application of supercomputers and is based on implicit monotonic approximation schemes and a modified Newton–Raphson method for solving nonlinear difference equations. By this method, the development of three-dimensional perturbations in the boundary layer over a flat plate and in a near-wall flow in a compression corner is studied at the Mach numbers of the free-stream of $\mathrm{M} = 5.37$. In addition to pulsation characteristic, distributions of the mean coefficients of the viscous flow in the transient section of the streamlined surface are obtained, which enables one to determine the beginning of the laminar-turbulent transition and estimate the characteristics of the turbulent flow in the boundary layer. 
@article{ZVMMF_2016_56_6_a11,
     author = {I. V. Egorov and A. V. Novikov},
     title = {Direct numerical simulation of laminar-turbulent flow over a flat plate at hypersonic flow speeds},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1064--1081},
     publisher = {mathdoc},
     volume = {56},
     number = {6},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_6_a11/}
}
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I. V. Egorov; A. V. Novikov. Direct numerical simulation of laminar-turbulent flow over a flat plate at hypersonic flow speeds. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 6, pp. 1064-1081. http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_6_a11/