Geodesic
An explicit-iterative scheme for the time integration of the Navier--Stokes equations
Matematičeskoe modelirovanie, Tome 32 (2020) no. 4, pp. 57-74

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A new integration algorithm is proposed for the time-dependent Navier–Stokes equations of compressible flows. We propose operator splitting method to split the equations into convection and diffusion parts which are solved successively at each time step. The convection part is solved by the Godunov method, the diffusion part is solved by the explicit-iteration Chebyshev scheme which has no stability restriction on the time-step size. The resulting scheme ensures the fulfillment of the main conservation laws on arbitrary unstructured grids. The explicit nature of the calculations ensures the efficiency of the use of the scheme in various parallel technologies.
Keywords: numerical simulation, Navier–Stokes equations, splitting method, Chebyshev explicit-iterative scheme. 
@article{MM_2020_32_4_a4,
     author = {V. T. Zhukov and O. B. Feodoritova and N. D. Novikova and A. P. Duben},
     title = {An explicit-iterative scheme for the time integration of the {Navier--Stokes} equations},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {57--74},
     publisher = {mathdoc},
     volume = {32},
     number = {4},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2020_32_4_a4/}
}
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V. T. Zhukov; O. B. Feodoritova; N. D. Novikova; A. P. Duben. An explicit-iterative scheme for the time integration of the Navier--Stokes equations. Matematičeskoe modelirovanie, Tome 32 (2020) no. 4, pp. 57-74. http://geodesic.mathdoc.fr/item/MM_2020_32_4_a4/