Geodesic
Application of splitting algorithms in the method of finite volumes for numerical solution of the Navier--Stokes equations
Sibirskij žurnal industrialʹnoj matematiki, Tome 21 (2018) no. 3, pp. 60-73

Voir la notice de l'article provenant de la source Math-Net.Ru

We generalize the splitting algorithms proposed earlier for the construction of efficient difference schemes to the finite volume method. For numerical solution of the Euler and Navier–Stokes equations written in integral form, some implicit finite-volume predictor-corrector scheme of the second order of approximation is proposed. At the predictor stage, the introduction of various forms of splitting is considered, which makes it possible to reduce the solution of the original system to separate solution of individual equations at fractional steps and to ensure some stability margin of the algorithm as a whole. The algorithm of splitting with respect to physical processes and spatial directions is numerically tested. The properties of the algorithm are under study and we proved its effectiveness for solving two-dimensional and three-dimensional flow-around problems.
Keywords: Euler and Navier–Stokes equations, finite-volume scheme, splitting algorithm, supersonic flow, shock wave. 
@article{SJIM_2018_21_3_a5,
     author = {V. M. Kovenya and P. V. Babintsev},
     title = {Application of splitting algorithms in the method of finite volumes for numerical solution of the {Navier--Stokes} equations},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {60--73},
     publisher = {mathdoc},
     volume = {21},
     number = {3},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2018_21_3_a5/}
}
TY  - JOUR
AU  - V. M. Kovenya
AU  - P. V. Babintsev
TI  - Application of splitting algorithms in the method of finite volumes for numerical solution of the Navier--Stokes equations
JO  - Sibirskij žurnal industrialʹnoj matematiki
PY  - 2018
SP  - 60
EP  - 73
VL  - 21
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SJIM_2018_21_3_a5/
LA  - ru
ID  - SJIM_2018_21_3_a5
ER  - 
%0 Journal Article
%A V. M. Kovenya
%A P. V. Babintsev
%T Application of splitting algorithms in the method of finite volumes for numerical solution of the Navier--Stokes equations
%J Sibirskij žurnal industrialʹnoj matematiki
%D 2018
%P 60-73
%V 21
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SJIM_2018_21_3_a5/
%G ru
%F SJIM_2018_21_3_a5
V. M. Kovenya; P. V. Babintsev. Application of splitting algorithms in the method of finite volumes for numerical solution of the Navier--Stokes equations. Sibirskij žurnal industrialʹnoj matematiki, Tome 21 (2018) no. 3, pp. 60-73. http://geodesic.mathdoc.fr/item/SJIM_2018_21_3_a5/