Geodesic
Preconditioning of Navier–Stokes equations in the computation of free convective flows
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 12, pp. 2109-2122

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Specific features of simulation of free convective flows of viscous compressible fluids based on the full Navier–Stokes equations are considered. The finite volume discretization of the Navier–Stokes equations in the case of low Mach numbers is discussed. To stabilize the numerical computations, preconditioning, which is based on the use of physical variables, and the dual time stepping method, which introduces internal iterations on pseudotime, are employed. The capabilities of the proposed approach are demonstrated on the example of simulation of free convection in a gap between coaxial cylinders. 
@article{ZVMMF_2015_55_12_a12,
     author = {K. N. Volkov and V. N. Emel'yanov and A. G. Karpenko},
     title = {Preconditioning of {Navier{\textendash}Stokes} equations in the computation of free convective flows},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {2109--2122},
     publisher = {mathdoc},
     volume = {55},
     number = {12},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_12_a12/}
}
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K. N. Volkov; V. N. Emel'yanov; A. G. Karpenko. Preconditioning of Navier–Stokes equations in the computation of free convective flows. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 12, pp. 2109-2122. http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_12_a12/