Geodesic
A Finite Difference Predictor-Corrector Scheme for Numerical Solution of~Navier--Stokes Equations for Compressible Heat-Conducted Gas
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 11 (2011) no. 4, pp. 32-48

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In the paper a modification of a finite difference predictor-corrector scheme for numerical solution of compressible Euler and Navier–Stokes equations is proposed. The scheme is based on a special approximation at predictor's stage which needs a minimal number of operations by a node of grid. High stability of the scheme was achieved using an approximation in agreement with the operators at predictor's and corrector's stages. There were studied basic properties of finite difference schemes and some advantages of proposed method were demonstrated. Obtained results for the problem of supersonic channel flow and the flow beyond a backward facing step confirmed a sufficient accuracy and efficacy of the method.
Keywords: Euler and Navier–Stokes equations, finite difference scheme, predictor-corrector method. 
@article{VNGU_2011_11_4_a3,
     author = {V. M. Kovenya and M. P. Kuzmin and R. S. Poltoratskiy},
     title = {A {Finite} {Difference} {Predictor-Corrector} {Scheme} for {Numerical} {Solution} {of~Navier--Stokes} {Equations} for {Compressible} {Heat-Conducted} {Gas}},
     journal = {Sibirskij \v{z}urnal \v{c}istoj i prikladnoj matematiki},
     pages = {32--48},
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     volume = {11},
     number = {4},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VNGU_2011_11_4_a3/}
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V. M. Kovenya; M. P. Kuzmin; R. S. Poltoratskiy. A Finite Difference Predictor-Corrector Scheme for Numerical Solution of~Navier--Stokes Equations for Compressible Heat-Conducted Gas. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 11 (2011) no. 4, pp. 32-48. http://geodesic.mathdoc.fr/item/VNGU_2011_11_4_a3/