Geodesic
The splitting algorithm in finite volume method for numericai solving of Navier--Stokes equations of viscous incompressible fluids
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 14 (2021) no. 4, pp. 519-527

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For the numerical solution of the Navier–Stokes equations, written in an integral form, an implicit of finite-volume algorithm is proposed, which is a generalization of previously proposed differences schemes. Using the integral form of equations allowed to ensure its conservatism, and the technology of splitting — the economy of the algorithm. The numerical test of the algorithm on the exact solution, in problems about the viscosity flow in the cavern with a moving lid and the current of the heated walls of the channel, confirmed the sufficient accuracy of the algorithm and its effectiveness. The work is presented in the issue of the memory of Prof. Yu. Ya. Belov.
Keywords: Navier–Stokes equations, viscous flows, finite-volume method, splitting algorithms. 
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     author = {Viktor M. Kovenya and Daniel Tarraf},
     title = {The splitting algorithm in finite volume method for numericai solving of {Navier--Stokes} equations of viscous incompressible fluids},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
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     volume = {14},
     number = {4},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2021_14_4_a13/}
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Viktor M. Kovenya; Daniel Tarraf. The splitting algorithm in finite volume method for numericai solving of Navier--Stokes equations of viscous incompressible fluids. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 14 (2021) no. 4, pp. 519-527. http://geodesic.mathdoc.fr/item/JSFU_2021_14_4_a13/