Geodesic
Parameter-free method for computing the turbulent flow in a plane channel in a wide range of Reynolds numbers
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 9, pp. 1545-1558

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Near-wall turbulence in a plane channel at high Reynolds numbers is studied by applying direct numerical simulation. A new numerical algorithm is proposed in which convective fluxes are explicitly approximated using the CABARET scheme and two grid elliptic equations are solved in order to satisfy the incompressibility condition. The equations are of high dimension and are solved by employing a fast direct method that can be efficiently parallelized. In contrast to most methods, including spectral ones, the CABARET scheme does not involve any tuning parameters. It has a compact stencil, which simplifies setting boundary conditions and improves the efficiency of parallelization in computations on multiprocessor computer systems. Numerical results are obtained in a wide range of Reynolds numbers and are compared with experimental data and numerical results of other authors. The error in the computed drag coefficient for turbulent flow is examined as a function of grid characteristics. 
@article{ZVMMF_2015_55_9_a9,
     author = {D. G. Asfandiyarov and V. M. Goloviznin and S. A. Finogenov},
     title = {Parameter-free method for computing the turbulent flow in a plane channel in a wide range of {Reynolds} numbers},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1545--1558},
     publisher = {mathdoc},
     volume = {55},
     number = {9},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_9_a9/}
}
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D. G. Asfandiyarov; V. M. Goloviznin; S. A. Finogenov. Parameter-free method for computing the turbulent flow in a plane channel in a wide range of Reynolds numbers. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 9, pp. 1545-1558. http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_9_a9/